Are you looking for custody or protection? While the granting of a Domestic Violence Restraining Order can facilitate a parent obtaining sole legal and physical custody (Fam C §3044), this should not be the genesis of your petition.
There is no cost to request a DVRO, but if and when the Temporary Restraining Order is granted, the father will not be permitted to have any contact with you, and likely the child, so you can expect that he will abrogate all financial support, unless ordered otherwise by the judicial officer.
The burden of proof is very low to obtain a restraining order, particularly the TRO, but you will still need solid evidence. He has witnesses that you "abused" him, and you have no witnesses of when you were "abused" by him, so this will present a challenge to you, particularly if he is represented by counsel.
You should see if the court in SF has a family law facilitator. You might also want to see a women's shelter in SF. The shelter might be able to provide some degree of legal assistance
The above is not intended as legal advice. The response does not constitute the creation of an attorney client relationship as this forum does not provide for a confidential communication.