Dear Sammy:
I suggest that you contact any and every governmental agency (as well as any attorney) that can help you bring about the situation where the only way for your daughter’s to see her father would be under supervised visitations (supervised by child protective services personnel, or the like), so that she is never alone with him.
Based on his domestic violence record, and any other record of his behavior that point to the likelihood of him neglecting and/or abusing your daughter, work toward the supervised visitations I mentioned.
If you clearly see that your daughter was abused while in his care (or lack of care), seek court intervention right away and refuse to hand her to him (while keeping your daughter and yourself safe, consider the protection of a shelter for abused women, if needed).
For as long as he does spend time alone with your daughter, take notes of all that you observe about the visits, and take photos of your daughter before and after you hand her to him.
anita