*245 OPINION
1. Children, Youth and Families Department (the Department) joins Father in the appeal of an order continuing legal custody of his children with the Department after abuse and neglect charges against him had been dismissed. Mother and the guardian ad litem object to the automatic placement of children with Father. We affirm in part and reverse and remand this matter in part with instructions. We affirm the portion of the trial court’s decision to continue the placement of the children with the Department until an investigation of the Father’s fitness and the allegations of abuse is completed. See NMSA 1978, § 32A-4-20(J) (1997). We reverse and remand in part to Children’s Court, wherein the Department shall investigate both the underlying allegations of abuse and current fitness of Father. We additionally instruct the Children’s Court to include Father in the children's treatment plan.
BACKGROUND
2. The original abuse and neglect petition was filed in Washington state after the youngest child suffered apparent child abuse. In the findings of fact entered by the Superi- or Court in Washington, the court made no specific finding as to the identity of the perpetrator of the injuries to the youngest child, but did find that Father had acknowledged shaking the baby but with no intent to inflict injury. Because father was in the Navy, a military criminal investigation was initiated, but no specific resolution of that investigation is part of the record. After the hearing, the court ordered that the child remain in Mother’s care under the supervision of the Washington State social services agency. Father was no longer in the home and Mother was seeking a divorce. After psychological evaluation the agency ordered counseling for both parents and parenting classes, as well as stress and anger management for Father. Mother subsequently moved to New Mexico, and was to continue to cooperate with the Department in New Mexico. Father remained in Washington.
3. In June 1995, after an attempted suicide by Mother, the Department filed a petition for abuse and neglect, naming both parents, and the children were taken into protective custody. The suicide attempt, coupled with the Washington incident, was the basis for the petition. A guardian ad litem was appointed for the children, and both parents were served with notice of the hearing. Mother did not appear at the hearing, but was represented by counsel; Father did not appear and was not represented by counsel. After the hearing a default judgment against both parents was entered adjudicating the children to be neglected and abused and ordering custody to remain with the Department. Before the disposition hearing, Father filed a motion to set aside the default judgment against him, which was granted conditioned on Father’s appearance at all future hearings.
4. In November 1995, a disposition order was entered regarding Mother which continued legal custody in the Department and included findings of fact and a treatment plan. The findings of fact made no mention of Father, and the treatment plan did not include Father. The treatment plan continued the confinement of the oldest child at a residential treatment center where he was making limited progress, and the two younger siblings remained in foster care. A recommendation was made that the two younger children be tested for developmental delays and learning deficits. In addition, the plan required an interaction assessment of the children with Mother and a schedule of visitation with her. It appears that there was little, if any, contact between the children and Father.
5. After the hearing, the trial court found that the oral motion to dismiss Father was well taken, but the requested findings were not. Specifically, the Department requested a finding that the Department was required to release the children to Father because they did not intend to pursue adjudication against Father. In denying the Department’s motion, the trial court ordered that legal custody should remain with the Department unless or until the domestic relations eourt handling the parent’s divorce determined that custody was appropriate with Father or when the children’s therapist deter*246mined that the children’s needs could be met by Father. Father appeals that order.
DISCUSSION
6. Father argues that he should be given custody of the children because no evidence was presented in support of the allegation of abuse and neglect or of his being an unfit parent. In support of his argument Father cites In re Mary L., 108 N.M. 702, 705, 778 P.2d 449, 452 (Ct.App.1989), in which we held that the noncustodial parent was entitled to custody unless the Human Services Department could establish a lack of fitness of the parent. However, in Mary L., there was absolutely no factual predicate giving rise to any suspicion of neglect or abuse, id. at 705-06, 778 P.2d at 452-58, whereas, in this case, there is a factual predicate sufficient to retain temporary custody of the children. Section 32A-4-20(J). Once the children have been adjudicated to be abused or neglected, and the parents are contesting custody, the dispute is between the parents. In which case, the court is required to follow the rule of best interests of the children. Schuermann v. Schuermann, 94 N.M. 81, 83, 607 P.2d 619, 621 (1980); Ettinger v. Ettinger, 72 N.M. 300, 303, 383 P.2d 261, 263 (1963). The State has established that the children are in need of services; the Department has an obligation to assure that the children receive those services.
7. The two younger children were in foster care and being screened for purposes of assisting in educational development. Although the middle child has no known illnesses or psychiatric treatment history, the youngest child is in a different situation. The youngest child was admitted to Children’s Hospital and Medical Center in Washington State when she was eight-weeks old for severe head trauma and seizures. This occurred on February 7, 1994. The district court’s uncontested findings of fact indicate the following in regard to that incident. First, neither parent had a reasonable explanation for the injury, while experts at the hospital stated that in their opinion the injury was non-accidental and they attributed it to child abuse. Second, a doctor at the Children’s Hospital stated that in his opinion the injury was so serious, it suggested out-of-control violence. He reported that it would be difficult to assess the exact degree of harm but “that she would be a pretty damaged child.” Third, as previously noted, according to the Washington State court, Father did acknowledge shaking the youngest child without intending to injure her. Currently the child has other medical problems which require vigilant “caretakers” to assure that she receives prompt medical care.
8. Given the condition of these children and the extent of their need for services, the Department has a responsibility to investigate even a natural parent when allegations of such abuse have been made. The presumption that custody should go to the natural parent is never conclusive and custody must be governed by the best interests of the children. In re Adoption of J.J.B., 119 N.M. 638, 652, 894 P.2d 994, 1008 (1995). “ ‘In New Mexico, there is a strong tradition of protecting a child’s best interests in a variety of circumstances.’ ” Sanders v. Rosenberg, 1997 NMSC 002, ¶ 10, 122 N.M. 692, 930 P.2d 1144 (quoting In re Adoption of Francisco A, 116 N.M. 708, 713, 866 P.2d 1175, 1180 (Ct.App.1993)). In dealing with children, the rule of “best interest of the children” is essentially equitable. See Sanders, 1997 NMSC 002, ¶ 10, 122 N.M. 692, 930 P.2d 1144. A court of equity has the power of devising a remedy to fit the circumstances of the situation. See In re Adoption of Francisco A, 116 N.M. at 713-14, 866 P.2d at 1180-81. Such is the case here. Additionally, Section 32A-4-20(J) allows for a court to make a custody determination while awaiting a determination or report regarding a parent’s alleged abuse or neglect of a child. Given these initial factual findings and the allegations made by the Department, the Department has a legal duty to investigate and the court has both an equitable and statutory responsibility to safeguard the children, including granting the Department legal custody for the time being, until the investigation is complete.
9. The Department made serious allegations of child abuse relating to Father. The *247Department offered findings of fact which were adopted by the trial court and have not been contested. Those allegations include the fact that when the child was admitted to the hospital the parents had no reasonable explanation for her injuries. A doctor (who is a child abuse and neglect consultant at Children’s Hospital) found that the child had suffered an inflicted head injury that was non-accidental and suggested out-of-control violence and that the child’s doctor does not know the exact extent of her injuries but stated that she is a pretty damaged child. The findings of fact also show that Father admitted to shaking his daughter without the intention to inflict injury. All of these allegations create a sufficient factual foundation for the Department to investigate and for the court to invoke the remedies under statute and equity, if necessary, to protect the child in the interim. Section 32A-4-20(J) provides:
On the court’s motion or that of a party, the court may continue the hearing on the petition for a reasonable time to receive reports and other evidence in connection with disposition. The court shall continue the hearing pending the receipt of the predisposition study and report if that document has not been prepared and received. During any continuances under this subsection, the court shall make an appropriate order for legal custody.
This gives the trial court sufficient authority to leave custody with the Department, at least on a temporary basis, until the investigation is completed.
10. Father argues that he is entitled to custody of his children because no evidence of his being unfit or any proof of the allegations in the petition have been presented. He asserts a violation of due process and a liberty interest in raising his children. We agree that there is a clearly established right to the integrity of the family, however, the parameters of the right are not absolute. See Oldfield v. Benavidez, 1994 NMSC 006, ¶ 15, 116 N.M. 785, 867 P.2d 1167. The law also supports the notion that the welfare of the children is paramount to the resolution of the case. See In re Adoption of J.J.B., 119 N.M. at 652, 894 P.2d at 1008.
11. If the trial court were attempting to make a final determination of custody based upon abuse or neglect and based upon this record only, we would agree with Father that there lacks a sufficient predicate as outlined in Mary L. But the trial court did not do so below. The trial court attempted to defer to the domestic relations proceeding for a final determination. In that respect, we think the trial court erred because it is the Department and the Children’s Court who collectively have the responsibility to make a determination, one way or another, with respect to both allegations of abuse and the welfare of the children. It is the Department which has the statutory authority and the financial resources to see this matter to a conclusion. We ought not burden the domestic relations court with that responsibility.
12. Therefore, we affirm the trial court’s determination to continue custody in the Department until the Children’s Court can investigate and determine the proper placement of the children. Additionally, to that limited extent only, we reverse the order of the Children’s Court below and remand for further proceedings below before the Children’s Court pursuant to Section 32A-4-20(J), wherein the Department shall investigate both the underlying allegations of abuse and the current fitness of Father subject to the supervision of the Children’s Court, and that ultimately the Children’s Court may make the necessary findings and conclusions with regard to Father’s fitness to be a legal custodian.
13. We also instruct the Children’s Court to revise the children’s treatment plan to include the Father pending the Department’s investigation and to require that Father participate in the treatment plan as a provision of his visitation rights. The court has the discretion to permit visitation rights to the parent. See NMSA 1978, § 32A-4-18(D)(2) (1993). NMSA 1978, Section 32A-1-3(A) (1993) requires the court to not only protect the children but also to “preserve the unity of the family whenever possible.” Father’s participation in the treatment plan would *248allow for Father’s visitation with the child and allow the Department to monitor Father’s interaction with the children. We therefore affirm in part and reverse and remand this matter in part with instructions for further proceedings not inconsistent with this opinion.
14. All motions held in abeyance are hereby denied.
15. IT IS SO ORDERED.
APODACA and BOSSON, JJ., concur.