Legal Question in Civil Litigation in California

Probably nothing. Legally, the dog is your son's property and you're not entitled to keep it. You can insist that he reimburse you for the costs of caring for the dog (assuming that you didn't already agree to absorb those costs), but I don't know if you would have the right to hold onto the dog while you await payment.

If we were talking about a child rather than a dog, you would be able to go to court and argue that you should be given custody. That doesn't necessarily mean you would win, but it does mean you would have the right to have a court decide the question. Child custody disputes are determined primarily according to the best interests of the child. Disputes over custody of property, however, are not determined according to the property's best interests -- even if the property is a dog.