You should speak with an attorney about a probate guardianship of the person, for which you would need to file appropriate paperwork with the Superior Court. The court filing for guardianship cases can be quite overwhelming for non-lawyers and requires that notice be given to the baby's father as well as certain relatives. A Caregivers Affidavit Authorization is another option that does not require court involvement, but whether or not it is a suitable alternative to guardianship in your...
There are domestic violence shelters that have great facilities and provide an array of support services for mother and child. To find out more about the shelters in your area, you should dial 211. This is a free phone service that operates 24/7 and can direct you to resources in your area. Best wishes to you.
Whether or not you have a criminal history is irrelevant. If you are exposing your daughter to dangerous situations, DCFS can remove your child. You will be appointed an attorney to represent you at your first Juvenile Court hearing. You don't want to miss this hearing if you want to try to get your daughter back immediately. You also have the right to hire your own attorney. There is good information about the Juvenile Dependency process at the CA Courts website.
You can make requests to the prosecuting agency or DA's office, but ultimately they represent the People of the State of CA and will do what is in the interest of the People. They do not represent you. They may take your opinion and wishes into consideration, but if for example he has had prior DV against you or other women, they may want to pursue the case against him if there is strong evidence. They can subpoena you to appear in court, and if you do not appear, you may face monetary sanctions.
To obtain a court judgement establishing parentage, you would need to file the proper paperwork with the county court, usually where the child lives, including the FL 200 as Mr. Conviser mentioned. You did not say whether the father would dispute his paternity or not. Filing the paperwork gives the alleged father an opportunity to respond and dispute paternity if that is his position. He could request a DNA test as part of this process. There are Self-Help Centers in the courthouses to help...
There are two separate cases you would need to file. You would first need to file a Petition to Terminate Parental Rights with the Superior Court. If the biological father consents, the process is fairly straightforward. His parental rights would be terminated by the judge, permanently freeing him of any parental responsibilities, including child support. Your new spouse could then file for a Stepparent Adoption with the Superior Court.
I agree that any forms must be stamped/filed with the court clerk in the county that the action was initiated in. The form can be found online at http://www.courts.ca.gov/documents/dv120.pdf
and you may also be able to mail it in along with the copies and self-addressed stamped envelope instead of going in person to file. Call the clerk's office and ask before you make the trip. You would need to appear for the hearing in that county, not in your county.
He can certainly file a request for visitation or custody, but whether a court would grant visitation or some degree of legal or physical custody depends on many factors. It is also possible that it may begin as supervised visitation and develop further depending on how the visits go.
If the police discover evidence of child abuse, the case would be referred to the DA's office to review and determine whether child abuse charges should be filed against the stepmom. Depending on the specific facts, they could be misdemeanors or felonies.