Minnesota's laws with respect to custody of minor children are gender neutral. They do not, however, address sexual orientation because the sexual orientation of one or both parents should not be an issue.
In a custody matter the court is guided by the "best interests" standard found at Minn. Stat. § 518.17. . See the FAQ "How is Custody Decided?" for the detailed explanation of the best interests standard.
What will be relevant is the quality of the relationship that each parent has with the minor child. Custody of your minor children is a very emotional issue for both parents. Generally speaking, both parents are heartsick at the thought of not having their children with them every day and they equate this with legal and physical custody. The children are equally distraught at the thought of not seeing both parents every day. When a family is broken, things must change, not the least of which is deciding on a parenting schedule for both parents. The objective should be to make those changes so they have the minimum possible negative impact on the children. The very best thing you can do for your children is to put your hard feelings aside, at least where they will impact the children, and try to work out a parenting time arrangement that will meet the children's needs.