If you and your ex-spouse agree to change custody of the children, you should make a motion to the court to change custody and support orders. Otherwise, you are still responsible for paying support to the other parent, even if you actually have custody of the children. Custody is sometimes changed if the custodial parent allows the children to live with the non-custodial parent for a much longer time than was ordered for parenting time.
Effective August 1, 2013, the law in Minnesota allows same sex couples to get married or divorced in this state. To file for divorce in Minnesota, at least one party must be living in Minnesota for at least 180 days before starting the divorce case. A same sex couple may also file for divorce in Minnesota if they got married in Minnesota on or after August 1, 2013, and each party to the marriage now lives in a state that does not allow the dissolution of the parties' same sex marriage. See Minn. Stat. § 518.07, subd. 2.