Legal Question in Family Law in California

The birth certificate doesn't matter. What matters is whether he has been legally determined to be the father. That is done one of two ways. Either he and the mother sign a Declaration of Paternity and file it, or one of them files a legal proceeding in Family Court to establish paternity. Until he is legally on record as the father, he has no rights and the mother has sole rights. Once he has legally established paternity he has the same rights, and obligations including child support if applicable, that a divorced father has. That would include the right to ask for custody or visitation. Once a custody or visitation schedule is ordered, he would have the right to object to a move that interfered with that schedule. He would never have a right to prevent the mother from visiting relatives on her custodial time.