There's not really anything you can do in advance because he would need to be served with a summons & if he's not in the country, you can't serve him. That said, upon his return, if he files, you may counter-file for an order of protection (if warranted) and a request that his visitation be supervised. Nevertheless, for a full assessment, please schedule a consultation with a NYC Child Custody attorney.
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Your issues are complicated. I think what you really need to do is consult a family lawyer. You can file a petition for modification of the existing visitation order and you can also file a petition for enforcement of the child support order. If you have no idea where the NCP is you can request an order for substituted service (by publication) of the ncp. That way you can have your orders all lined up if and when the NCP shows up again. Simply having a passport for the child is not enough for the NCP to take the child out of the country. The NCP needs your consent. Talk to a family law attorney. Good luck.
If there is an arrest warrant for the NCP, it is unlikely that he will be returning to assert a visitation claim. If he does return and files for visitation, you must immediately hire a family court attorney to represent you. Until he files something, I would do nothing. If you have a child support order, arrears will continue to accrue. If he returns, you can seek to have it enforced. It is unlikely that anything fruitful will come from tying to go after the arrears while he is hiding out in another country and you don't know his whereabouts.
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