J.W.
That you moved back can change things. Just to make sure you are doing everything right I would go back to court and spell things out.
Before you do anything though, talk to their dad. My ex is a bit of a tool but the courts wouldn't entertain any requests until I made the effort to talk to him.
What I know about big moves is this, had I needed to move out of state when we divorced the court would have given me primary custody. If I wanted to move somewhere else I would have been required to petition the court again, you did not do that when you moved back.
I am only saying this because when it comes to potentially being accused of kidnapping it is just worth it to have the courts blessing.
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R., you could do it yourself but it is better to have an attorney dot the i s for you. Most good attorneys have a flat fee for something this simple but then you know it is properly drafted and properly filed.