Come on now, child support? He isnt on the birth certificate, there is no treaty with the USA and he has to declare fatherhood in person with two witnesses. For HER to insinuate child support on an anonymous person SHE would have to establish and proof paternity at her own expense.
Domestic violence? Needs a time and place. Dude hasnt been in country in a year.
Stop fear mongering. She probably wants to have the child get US citizenry and then she could try to use that for a familial visa in the future when the thing with the European fails
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Come on now, he is asking for advise and this is obvious that she is going after something she is not stating.
DR laws are not exactly by the book, but they will force you to take a paternity test or you will be arrested. I know of this happening to a General who denied a son, so the laws or enforcement are pretty favorable to women. Also in DR law the kids automatically get part of the inheritance (very difficult to get around that). On the abuse side which I didn't think about, also know about a lot of false accusations on that front.
I would really suggest figuring out how to get a paternity test done remotely and then determine the support, but if you go back good luck to you. If it doesn't smell right and she can't even give you a consistent reason why chance being in a mess that you wouldn't believe.