You shouldn't try to handle a custody case on your own. If his rights have not been terminated, the court will allow him to reunify with the child. Whether or not that is supervised, or therapeutic depends on the strength of your facts. His request for sole is certainly frivolous given the facts you set forth.
Your first issue is to get a protective order to stop him from beating you again. The District Attorney has a department to assist in this.
After that, get legal help. Handled properly, custody is unlikely from an absentee violent father, but you really need a lawyer.