You release the children to the father and ONLY the father. His GP can not take his visitation just to make it look good.
Also, you have more than enough information to either stop visitation or change it due to the neglect and his new spouse.
He is moving, if he wants to see the child then he comes back and see them for the weekend. Do not let him take the children away and certainly do not let him have anymore that is currently court ordered. Let him petition the court to change it..
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Psst.. I am not an attorney, and even if I was, I would not tell you. What I am giving you is not legal advice in anyway. For proper legal advice, retain a person who openly admits they are an attorney.