When a couple divorces or separates, and has no children in common, then either party is free to move, or live, where they choose and/or where they can afford to live. If the parties have no minor children (children under age 18), the same goes. This contemplates that the adult child(ren) can live where they please, since they are on their own under the law.
If the couple share a minor child, or children, then it is also the case that either party is free to move where they choose. However, the child(ren) will not move out of state without either the other parent’s consent, or the court’s permission. So if a co-parent wishes to move out of state, that is fine, if the child(ren) stay(s) behind living (primarily) with the other parent in Minnesota. If the moving parent wants the child(ren) to move with them, then they need the other parent’s consent, or the court’s permission.
The current law requires the moving parent to establish by a preponderance of the evidence that the move is in the child(ren)’s best interests. The burden of proof is on the moving parent. (There is an exception to that if there is domestic violence involved, in which case the allegedly abusive parent carries the burden of proof.)