829 P.2d 660 (1992)
113 N.M. 581
A.C., Petitioner-Appellant,
v.
C.B., Respondent-Appellee.
No. 12335.
Court of Appeals of New Mexico.
January 30, 1992.
Certiorari Denied March 24, 1992.
Ruth B. Cohen, Albuquerque, for petitioner-appellant.
Janice D. Paster, Albuquerque, for respondent-appellee.
Gerald R. Bloomfield, Albuquerque, for amicus curiae Legal Research Co., Ltd.
Paula L. Ettelbrick, Marian Rosenberg, Lambda Legal Defense and Educ. Fund, Inc., New York City, Maria Gil de la Madrid, National Center for Lesbian Rights, San Francisco, Cal., Elizabeth Stacy Vencill, Albuquerque, for amici curiae LLDEF & NCLR.
Phillip B. Davis, Civil Liberties Union of New Mexico, Albuquerque, William B. Rubenstein, American Civil Liberties Union Foundation, New York City, Ann C. Scales, Cooperating Atty., Albuquerque, for amici curiae CLUNM & ACLUF.
OPINION
BIVINS, Judge.
Petitioner-appellant's motion to exclude the names of the parties and the child from any opinion written in this matter is granted. The opinion in this case shall be captioned A.C. v. C.B. The parties shall be referred to as the biological mother and Petitioner. The child who is the subject of these proceedings shall be referred to as the child without further identification.
Petitioner appeals from an order of the district court denying her motion under Rule 60(B)(3) of the New Mexico Rules of Civil Procedure, SCRA 1986, 1-060(B)(3), to reopen the judgment of the district court, or, in the alternative, to enforce an oral settlement agreement between the parties. We reverse and remand to the district court for further proceedings consistent with this opinion.
I. BACKGROUND
Petitioner's verified Rule 60(B)(3) motion provides most of the factual background giving rise to this litigation. Petitioner, a woman, and Respondent, the biological mother, lived together for approximately fourteen years before separating on July 1, 1987. About seven years earlier, in 1980, the parties, according to Petitioner, entered into an oral agreement to raise a child as coparents. In September of 1980, the biological mother gave birth to the child, conceived through artificial insemination. Petitioner alleges that during the pregnancy she attended Lamaze classes, and after the birth she shared the responsibility of caring for the child. Petitioner also alleges that she spent the majority of her evenings and weekends with the child until the separation. Petitioner and the biological mother together set up a trust fund for the child's education, as well as a savings account and life insurance policy for the child's benefit. Petitioner alleges that she has shared the financial responsibility for raising the child.
Petitioner's motion to reopen the judgment alleges that the biological mother in her will named Petitioner as guardian and trustee of the child. Petitioner claims that the original coparenting agreement was renewed by the parties before their separation and honored until March 1988, the date Petitioner claims that the agreement was breached by severe restrictions on her claimed rights to visit and have contact with the child. Petitioner claims her offers of financial support for the child were refused.
As a result, Petitioner filed this action in October 1988, seeking joint legal custody and time-sharing. In March 1989, the court entered an order dismissing the petition with prejudice. The order was signed by the district judge and the attorneys for each party. The order states that "[t]he parties have entered into a settlement agreement providing for dismissal for this action with prejudice." About five months later, Petitioner filed a verified petition to set aside or reopen or, in the alternative, to enforce the settlement agreement under Rule 60(B)(3). The motion to reopen the judgment alleges that the matter was referred to the district court clinic which made certain recommendations. Petitioner alleges that, as a result of those recommendations, the parties entered into an oral agreement covering time-sharing, parenting classes for Petitioner, therapy, and mediation. According to Petitioner, counsel for the biological mother refused to reduce that agreement to writing. Petitioner claims that agreement formed the basis for the dismissal of her action with prejudice on March 23, 1989.
In response to the motion to reopen the judgment, the biological mother moved for summary judgment. The summary judgment motion sets up a number of legal defenses which challenge Petitioner's standing to claim any rights to the child. Attached to her motion for summary judgment is the biological mother's affidavit which denies the existence of any agreement made at any time regarding the child. The biological mother asserts her fitness as a parent and states that no legal relationship existed between the child and Petitioner that would confer any "rights, privileges, duties and obligations" on the latter.
Petitioner responded to the biological mother's motion for summary judgment asserting the existence of issues of material fact, i.e., whether agreements between the parties had been made, and whether Petitioner was a de facto parent. Petitioner attached her affidavit to the response which reasserts the agreements and provisions made regarding the child. Petitioner also attached a copy of the biological mother's will naming Petitioner as guardian and trustee of the child.
II. FINDINGS OF THE DISTRICT COURT
Following a hearing, at which no testimony was taken, the district court entered an order granting the biological mother's motion for summary judgment and affirming the earlier dismissal with prejudice. The minute order includes findings of fact. Those findings indicate that the district court considered the matter disposable on legal grounds without the need for an evidentiary hearing. The district court found that no valid legal marriage existed between the parties, there was no adoption of the child by Petitioner, and thus, Petitioner had no standing or enforceable rights. The district court recited the earlier dismissal and found Petitioner had not met her burden under Rule 60(B) to reopen the judgment. While determining that it need not address whether or not the parties entered into an enforceable contract, the district court concluded that, even "if some form of contractual relationship existed between the parties, it [was] not in the best interest of the minor child" and, therefore, not enforceable. The district court also upheld the constitutionality of New Mexico statutes that bear on the questions presented. This appeal followed.
III. DISCUSSION
A. General
Although Petitioner's response to the biological mother's motion for summary judgment raised factual issues regarding the agreements, we read the district court's minute order as resolving the issues on legal grounds.
The posture of this case presents a unique situation. A determination of Petitioner's rights depends on her first, establishing a basis for setting aside the order of dismissal and, assuming she is successful in doing so, second, establishing a basis for either shared custody or visitation. We are unable to review the merits of Petitioner's claims of entitlement to custody and visitation, or for that matter the merits of her Rule 60(B) motion, without factual determinations. Understandably, the district court, having concluded as a matter of law that no basis existed to set aside the dismissal, saw no need to decide factual questions.
While we refrain from making a definitive decision regarding Petitioner's claims at this time, we hold that she made a prima facie showing which, if proved, would justify setting aside the dismissal and authorize consideration of her right to continue her relationship with the child. Thus, on that basis, we reverse and remand.
We first address Petitioner's Rule 60(B) motion. Under that discussion, we decide first whether the district court had jurisdiction to entertain the motion and, second, whether Petitioner made a prima facie showing that would allow the district court to set aside the dismissal. Next, we consider the district court's determination that enforcement of the alleged settlement agreement would be contrary to the best interests of the child. Finally, we discuss Petitioner's request for alternative relief should the district court decline to enforce the alleged settlement agreement.
B. Petitioner's Rule 60(B) Motion
1. Jurisdiction
The biological mother argues that when the parties stipulated to a dismissal of the case with prejudice, the district court lost jurisdiction over the parties and the subject matter and could not thereafter decide any matters presented or enforce alleged stipulations of the parties. We recognize that the district court's control over a final judgment exists for a limited period of time. NMSA 1978, § 39-1-1 (Repl.Pamp.1991); SCRA 1986, 12-201. Section 39-1-1, however, has never been viewed as depriving the district court of jurisdiction to consider and resolve a subsequent timely motion under Rule 60(B). Wooley v. Wicker, 75 N.M. 241, 244-45, 403 P.2d 685, 687-88 (1965) (decided under NMSA 1953, § 21-9-1, the predecessor to NMSA 1978, § 39-1-1). In fact, the purpose of Rule 60 is "to provide a simplified method for correcting errors in final judgments" and to balance the competing principles of finality and relief from inequitable judgments. Phelps Dodge Corp. v. Guerra, 92 N.M. 47, 50, 582 P.2d 819, 822 (1978). We hold, therefore, that the district court had jurisdiction to consider the Rule 60(B) motion.
2. Denial of Motion
We turn next to the question of whether the district court properly denied the motion. The motion alleged, in essence, that the biological mother misrepresented her intention to abide by the settlement agreement once the case was dismissed with prejudice. We believe this allegation amounts to a prima facie basis for relief under Rule 60(B)(3). Unser v. Unser, 86 N.M. 648, 653-54, 526 P.2d 790, 795-96 (1974) (fraud under Rule 60(B) requires "a misrepresentation of a fact, known to be untrue by the maker, and made with an intent to deceive and to induce the other party to act upon it with the other party relying upon it to his injury or detriment"); Rios v. Danuser Mach. Co., 110 N.M. 87, 93, 792 P.2d 419, 425 (Ct.App.) (relief under Rule 60(B)(3) is available where court determines that misconduct of the opposing party substantially impeded movant's full and fair preparation of its case), cert. quashed, 110 N.M. 72, 792 P.2d 49 (1990). Thus, Petitioner's allegations of a settlement agreement and fraud give her standing to seek relief under Rule 60(B)(3).
Since Petitioner's motion to reopen the judgment is based on Rule 60(B)(3), and the parties disagree as to what, if any, stipulation or agreement was made between them before the dismissal, it will be necessary for the district court to conduct an evidentiary hearing. The burden is on Petitioner to establish an agreement with the biological mother which induced Petitioner to agree to dismissal. Cf. Kulla v. McNulty, 472 N.W.2d 175, 179 (Minn.Ct.App.1991) (petitioner failed to meet each statutory criterion for visitation). If the district court finds an agreement was made and finds fraud, misrepresentation, or other conduct on the part of the biological mother that induced Petitioner to agree to dismissal, the district court should then proceed to consider what rights, if any, are conferred on Petitioner by reason of any agreements made or actions taken.
C. The District Court's Determination That Enforcement of the Settlement Agreement Was Contrary to the Best Interests of the Child
The district court's order determined that, as a matter of law, the agreement was unenforceable because it was not in the best interests of the child. We hold that the district court could not make this determination on the record before it in this case.
This court has previously held that a parent may enter into an agreement with another person concerning the custody of a child. See In re Adoption of Doe, 98 N.M. 340, 346, 648 P.2d 798, 804 (Ct.App.) (agreement between natural mother and stepfather), cert. denied, 98 N.M. 336, 648 P.2d 794 (1982). It is true that a parent's power in this regard is not unlimited. Thus, for example, a parent may not sell a child into peonage. Bustamento v. Analla, 1 N.M. (Gild.) 255, 261 (1857) (court bound to set child free from improper restraint); see also Barwin v. Reidy, 62 N.M. 183, 196, 307 P.2d 175, 184 (1957) (sale of children constituted abandonment as a matter of law). Accordingly, agreements between parents and others concerning children are subject to judicial modification when such modification is in the best interests of the child. In re Adoption of Doe, 98 N.M. at 346, 648 P.2d at 804. Both parties recognize that any agreement between them concerning the child would be subject to judicial modification.
The district court's order in this case purports to determine that enforcement of the visitation provisions of the settlement agreement would, as a matter of law, be against the best interests of the child. A determination of the best interests of the child, however, must be made on the basis of evidence before the court. See, e.g., In re Jacinta M., 107 N.M. 769, 771, 764 P.2d 1327, 1329 (Ct.App.1988) (finding must be supported by evidence); Khalsa v. Khalsa, 107 N.M. 31, 36, 751 P.2d 715, 720 (Ct.App.) (harm to child cannot be assumed but must be demonstrated), cert. denied, 107 N.M. 16, 751 P.2d 700 (1988); Fitzsimmons v. Fitzsimmons, 104 N.M. 420, 423, 722 P.2d 671, 674 (Ct.App.) (court's ruling must be supported by evidence), cert. quashed, 104 N.M. 378, 721 P.2d 1309 (1986). We hold that, under New Mexico law, the district court erred in concluding that this type of an agreement is unenforceable as a matter of law. But see Sporleder v. Hermes (In re Z.J.H.), 162 Wis.2d 1002, 471 N.W.2d 202, 211 (1991) (holding similar agreement void on public policy grounds). Whether visitation would be against the best interests of the child is a factual determination that must be made on the evidence. See Rhinehart v. Nowlin, 111 N.M. 319, 329-30, 805 P.2d 88, 98-99 (Ct.App.1990) (affirming district court's determination that, on the facts before the court, court-mandated visitation by a stepmother would not be in the best interests of the children due to the high degree of conflict between stepmother and the father of the children).
In addition, while the record before us does not clearly indicate the existence of a lesbian relationship between the parties during the years they lived together, to the extent it may become an issue on remand, we hold that Petitioner's sexual orientation, standing alone, is not a permissible basis for the denial of shared custody or visitation. The appellate courts of this state have repeatedly held that evidence of sexual and associational conduct may be relevant to determining the best interests of the child, but is not, by itself, sufficient to make that determination. See, e.g., Boone v. Boone, 90 N.M. 466, 468, 565 P.2d 337, 339 (1977) (nonmarital sexual activity); Leszinske v. Poole, 110 N.M. 663, 670, 798 P.2d 1049, 1056 (Ct.App.) (marriage that is void as against public policy in New Mexico), cert. denied, 110 N.M. 533, 797 P.2d 983 (1990); Fitzsimmons, 104 N.M. at 426-27, 722 P.2d at 677-78 (nonmarital sexual activity). In addition, this court has previously indicated that a person's sexual orientation does not automatically render the person unfit to have custody of children. See, e.g., Jacinta, 107 N.M. at 771-72, 764 P.2d at 1329-30; In re Doe, 88 N.M. 505, 509-10, 542 P.2d 1195, 1199-1200 (Ct.App. 1975). Other jurisdictions have held in the context of dissolution proceedings that a parent may not be denied visitation solely on the basis of sexual orientation. See generally Caroll J. Miller, Annotation, Visitation Rights of Homosexual or Lesbian Parent, 36 A.L.R.4th 997 (1985 & Supp. 1991); Wanda E. Wakefield, Annotation, Initial Award or Denial of Child Custody to Homosexual or Lesbian Parent, 6 A.L.R.4th 1297 (1981 & Supp.1991). In short, the issue before the court is not the nature of the parent's sexual activities, if any, but whether and how those activities affect the child, if in fact they do. This is a factual issue that must be considered and resolved on specific evidence concerning the effect, if any, of the activity on the children; it cannot be resolved as a matter of law based on the perceived morality or immorality of the parent's conduct. See Boone, 90 N.M. at 468, 565 P.2d at 339; Fitzsimmons, 104 N.M. at 426-27, 722 P.2d at 677-78.
D. Alternative Relief If Settlement Agreement Unenforceable
Should the district court find fraud but determine that there is no enforceable settlement agreement, Petitioner asks that she be permitted to proceed with her original claim. As noted earlier, the biological mother challenges Petitioner's standing to claim any rights to the child. While guidance for the district court in this rapidly developing area of the law might be useful, we do not think it prudent to issue an advisory opinion, particularly without the benefit of the district court's findings of fact and conclusions of law. Thus, at this point in the proceedings, we consider only whether Petitioner has demonstrated a colorable claim to either shared custody or visitation.
Because the issues on appeal initially appeared to raise important questions regarding the rights of non-traditional parents, as well as other significant issues, this court invited amicus briefs. These briefs, as well as the briefs of the parties, have provided the court insight into the issues presented. See generally Katharine T. Bartlett, Rethinking Parenthood as an Exclusive Status: The Need for Legal Alternatives When the Premise of the Nuclear Family Has Failed, 70 Va.L.Rev. 879 (1984); Sandra R. Blair, Jurisdiction, Standing, and Decisional Standards in Parent-Nonparent Custody DisputesIn re Marriage of Allen, 28 Wn.App. 637, 626 P.2d 16 (1981), 58 Wash.L.Rev. 111 (1982-83); Elizabeth A. Delaney, Note, Statutory Protection of the Other Mother: Legally Recognizing the Relationship Between the Nonbiological Lesbian Parent and Her Child, 43 Hastings L.J. 177 (1991); Developments in the LawSexual Orientation and the Law, 102 Harv.L.Rev. 1508, 1628-42 (1989); Nancy D. Polikoff, This Child Does Have Two Mothers: Redefining Parenthood to Meet the Needs of Children in Lesbian-Mother and Other Nontraditional Families, 78 Geo.L.J. 459 (1989-90); E. Donald Shapiro & Lisa Schultz, Single-Sex Families: The Impact of Birth Innovations upon Traditional Family Notions, 24 J.Fam.L. 271 (1985-86); Stephanie H. Smith, Psychological Parents vs. Biological Parents: The Courts' Response to New Directions in Child Custody Dispute Resolution, 17 J.Fam.L. 545 (1978-79); Wendy E. Lehmann, Annotation, Award of Custody of Child Where Contest is Between Natural Parent and Stepparent, 10 A.L.R.4th 767 (1981 & Supp.1991). One in Petitioner's shoes may be able to establish deprivation of a legally recognized right to maintain some type of continuing relationship with the child. Cf. De Vargas Savings & Loan Ass'n v. Campbell, 87 N.M. 469, 472, 535 P.2d 1320, 1323 (1975) (injury sufficient to confer standing not limited to economic harm). We hold, therefore, that Petitioner has made a colorable claim of standing to seek enforcement of such claimed rights. Cf. Buness v. Gillen, 781 P.2d 985, 988 (Alaska 1989) (non-parent with a "significant connection" to the child has standing to assert custody claim); Nancy S. v. Michele G., 228 Cal.App.3d 831, 279 Cal.Rptr. 212, 215 n. 2 (1991) (rejecting earlier California opinion that lesbian lover lacked standing to seek custody and visitation). But see In re Z.J.H., 471 N.W.2d at 205 (nonparent lacked standing to seek custody or visitation); Alison D. v. Virginia M., 77 N.Y.2d 651, 569 N.Y.S.2d 586, 588, 572 N.E.2d 27, 29 (1991) (petitioner lacked standing because she was not a "parent" as defined by the statute).
E. Attorney's Fees
The biological mother asks this court to award her attorney fees for representation on appeal. This court, however, may only award attorney fees for representation on appeal if the award of such fees is authorized by statute or otherwise permitted by the appellate rules. SCRA 1986, 12-403; Alber v. Nolle, 98 N.M. 100, 108, 645 P.2d 456, 464 (Ct.App.1982). Biological mother cites no authority for the proposition that she is entitled to attorney fees on appeal. Accordingly, we do not consider her request. In re Adoption of Doe, 100 N.M. 764, 765, 676 P.2d 1329, 1330 (1984) (issues raised on appeal not supported by authority will not be reviewed).
IV. CONCLUSION
We wish to express our appreciation to amici, the Legal Research Co., Ltd., Lambda Legal Defense and Education Fund, Inc., the National Center for Lesbian Rights, the Civil Liberties Union of New Mexico, and the American Civil Liberties Union Foundation, for their excellent briefs.
We remand this action to the district court for further proceedings consistent with this opinion. The district court should first determine the merits of Petitioner's Rule 60(B)(3) motion. If granted, the court must then decide the terms of the settlement agreement made between the parties. Should the district court find no valid or enforceable agreement but also find that Petitioner was induced into dismissing her claim thinking there was such an agreement, the court should then determine what, if any, rights Petitioner may have to shared custody or visitation either under the settlement agreement or Petitioner's original claim. The court must, of course, consider the best interests of the child. No costs are awarded.
IT IS SO ORDERED.
MINZNER and BLACK, JJ., concur.