As others have said, best to check the requirements of all countries involved, not just the US. FWIW, IME the biggest headache is with the airlines, not the immigration authorities. I was once given the third degree by a QF agent when trying to check in my son (who was on a separate record) on a flight back to the US from OZ. Indeed, the TA refused to check him in until a supervisor was consulted and agreed it was none of her business where the child's mother was.