I am profoundly skeptical that, in a situation where Amy Bradley was made a sex slave and carried to term children born of these rapes, she the mother would not get custody. If she was mentally incompetent to parent, perhaps? But even then, I would imagine that authorities in the Caribbean would realize the terrible optics, and politics, of keeping an American woman terribly victimized in their country from her children.
Mind, all this assumes that her abductors would allow her to carry the pregnancies to term. (If, in fact, they let her live so long.)
Looking to Curaçao, the US State Department's 2024 report does suggest there are serious problems in the local government's response to trafficked women.
It should be noted that it also identifies the women subjected to sex trafficking as coming mainly from Hispanic countries in the Caribbean basin, with Venezuelans being especially common these days thanks to that country's breakdown. An Anglophone--an American, definitely--would stand out in this population.