I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear that this happened.
In order to get visitation with the child after it's born, he'll have to file for divorce. He does have the ability to file in New Mexico because that's where he lives and where they lived together when they were married. If paternity is disputed, then the judge will probably wait to grant the divorce until after the child is born, but that gives them time to try to work out a custody and visitation agreement on their own. He will be able to have his name added to the birth certificate if she doesn't list it for him, once a DNA test is obtained through the courts.
The problem with waiting to file for divorce until after the child is born is that, at that point, he'll need to file in New Jersey (where the child lives). And a person can't file for divorce in New Jersey until they meet the residency requirement, which means that the mother must have lived there for one year before your son files - and that means your son would be filing for divorce a few months after the child is born. I would understand if he didn't want to wait that long.
The courts start with a presumption that it is in the best interests of the child to have a relationship with both parents. Therefore, he should be able to get some visitation. When the baby is very young, he may need to travel to New Jersey to see the child. Since the mother made this necessary by moving across the country, he can ask that she be ordered to share the costs or deduct a portion of that travel expenses from child support. But he does have a right to see the child once he gets a court order.
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