any document pertaining to custody of the child that is not signed by a judge in a divorce/custody proceeding, even if notarized, is not an enforceable document. Meaning if he signs something saying you can go, he has the right to change his mind during the divorce. You can not move without his, and the court's permission. You need to file in the state you are in, and hope the judge sides with you on the petition to move.
Highly doubtful your ex will give you an uncontested divorce and sole custody of the child if he is abusive - it will just be a form of trying to control you by contesting everything, and filing for custody of his home, or refusing to allow your move.
I suggest you get an attorney - I forsee this getting ugly.I'm a family law attorney.
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