Legal Question in Family Law in California

You cannot prophylactically terminate a parent's rights. Unless and until he does something that would get the child permanently removed from his care by Child Protective Services, after failure of reunification services, you cannot terminate his parental rights, and unless you remarry and your husband wants to adopt her, the dad cannot even give up his rights voluntarily.

You may consider a motion to the court to restrict his contact with the child if his level of irresponsibility is elevated to endangering the child. If he is homeless, then his timeshare could be severely curtailed until he has housing and a place to visit with the child that is safe. I think it would be in your best interests to meet with a skilled family law attorney to properly evaluate your options.