Under NYS Law when can a divorced spouse who was awarded custody of the children relocate to another state?

Usually, to make a move the custodial parent will need consent of the other parent, or a court order. If the non-custodial parent objects to a proposed move (or an actual move), the non-custodial parent can file a petition in family court to stop the move and even ask for a habeas (to bring the children to court) and a warrant for the other parent's arrest. This is a serious issue and you should consult an attorney. Good luck!