Can the other parents move out of state without my permission?
If the parents are already divorced and/or there is a parenting agreement in place, then one parent cannot unilaterally move out of state with the minor children without the other parents consent. The parent themselves can move if they chose to, but only without taking the children with them.
If a couple is still married or there is no parenting agreement in place, then they could possibly move out of state without letting the other parent know or getting permission from the court. However, once the other parent finds out, they have the immediate right to go to court and ask for the return of the child while a parenting plan is sorted out through the courts.