The Family Division of the Superior Court shall have jurisdiction to hear and dispose of issues pertaining to parental rights and responsibilities, parent-child contact and child support in accordance with the provisions of 15 V.S.A. chapter 11 under the following circumstances:
(1) If two unmarried persons, who have adopted a minor child, terminate their domestic relationship; or
(2) If two unmarried persons, one of whom has adopted a minor child of the other, terminate their domestic relationship.