Legal Question in Family Law in California

She is better of giving the child her last name and not identifying the father. That would require him to file a paternity case to establish that he is the father before he could even contemplate doing anything else. A custody order would issue as part of the paternity case. He would then have to get your daughter's consent, or a court order, to get a passport for the child, and your daughter would have to accompany him or provide a notarized consent for him to get a visa for the child or to leave the country with the child. There is no guarantee that a foreign born parent can never game the system and illegally remove a child, but what I have outlined would put the most legal barriers possible in the way of him doing it.