I'm sure that they will have to use extradition to get the baby back, but so far the Bahamian gov't seems to be supporting Stern as the father. I am sure that they were doing whatever was deemed necessary to avoid extradition of the baby , since birth, maybe even before. She wasn't married to Stern, was she?
As long as the baby's undisputed mother was alive, the Bahamian government wouldn't have any reason to interfere with the decisions that the mother was making -- which apparently consisted of endorsing whatever Stern wanted to do. As far as I know, no US court has requested that the baby be returned to the US. That's likely to change very soon, and I don't think there's any reason to expect the Bahamian government to refuse to comply, in deference to the wishes of the non-Bahamian citizen, not-definitely-the-father Stern.
Extradition is not the right term for what our courts would order for the baby's return, though I'm not sure what is. If Stern interfered with the implementation of such an order, he would be committing a crime under US law, and would be subject to extradition. I'm virtually positive that the Bahamas is not one of the countries that doesn't honor child custody orders from the country of which the child is a citizen. I expect that Stern would be treated like Allison Quets, charged with kidnapping and extradited, if he did not return the baby to the US upon a court order to do so (presumably the order would actually go to the Bahamian government, but Stern appears to be the only one in a position to interfere with the baby's return).