In many situations ex-wives might end up using the threat to move away against you as a negotiating tactic for family court. Typically, if you already have a court order in place, this is something that must be approved by the judge before it goes very far, and as a result you can have a legal professional help you out in most situations. In some situations an ex-wife might choose to leave anyway, but with the assistance of the court she can be compelled to return.
Usually if someone is wanting to leave the state they need to notify their ex-spouse, and if they do not then they might end up in trouble with the court. Having a legal professional on your side to present evidence to the court with regard to what is going on around a move is very important. In many states the response time to these motions is around a month long, but you can expedite in some situations in the case of an emergency.
The action most people take is to hire a legal professional in order to see what their options are, and after that they bring the situation to the attention of the court. The failure to pursue any action could result in the children moving away, and this is something that can end up being permanent. Even if an ex-wife does end up moving the visitation rights will still apply and be enforced by the court.