Unfortunately if someone wants to fight for the purpose of fighting (i.e. because he wants to drag it out, not pay you a dime, make things difficult for you), you have no choice but to go along with the litigation process. If he refuses to leave and you cannot stay, then you should consider leaving. If your child is a minor, you'd be entitled to child support. If you're worried about him paying the support once it is ordered, you could seek an income deduction order or garnishment so that his child support is paid right to you from his employer. If he leaves the country then while the U.S. Order would still be valid and enforceable, obviously if he isn't here to enforce it on, then you would have a problem.
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