Without a custody arrangement are kids fair game?

My ex and I have been separated for 11 months. We have two children, aged 12 and 14. I was a SAHM for the last 6 years of our marriage and he moved out after and argument. He has controlled all money since then and I haven’t pushed the issue of an agreement because we were getting along “ok” without it.

I was offered a job in Georgia. I have had the kids with me the majority of the time and we had a verbal agreement for every other weekend. He refuses to entertain the idea of a move, but again, there is nothing in writing preventing me from taking the job. We have no family in this state and only relocated here 4 years ago. I do have family closer in that state.

If we sign an agreement and have it entered into the court addressing custody, but not a move, what would happen if I then gave him notice that I was going to take the job? I am not trying to interfere with his visitation, but I have to be able to support my kids.

Thank you.