Do I need approval to move out of state?

My ex has already left NC and moved to NY. We have a loose visitation schedule that allows him visitation every other Sunday, however he wants an even looser visitation schedule thats more like whenever he can be bothered from 930AM to 230PM. There is no restrictions listed in the custody agreement and I have sole physical and legal custody. My current husband is entering into the military and is more than likely not going to be stationed in NC. In the past my ex has said it would be fine if I moved(over text, multiple times) so do I need to get his ok to move once we find out where my husband will be stationed? Also, if I need proof of his ok would a notarized letter from him stating that he gives me permission to move be ok?

Yes, you can move out of state and you would not need approval unless your custody order or separation agreement addressing custody has a paragraph about moving out of state with the children. If so, you would need to refer to that paragraph and follow what it says about moving out of state. You would not need proof that your husband okays the move out of state unless your court order or separation agreement states so.