Can my children’s mother allow my kids to leave the state without my consent?

Leave the state for vacation, or move out of the state?  It depends on what the current order states.  Does the current order prohibit the children leaving the state for vacation?   If you are talking about moving the children out of the state, and the current order does not give her permision to do so, you can file a Petition/Motion with the court to Enjoin the children leaving the state.  Speak to an attorney for more specific advice on your situation.