This poor little girl has been abused by her father and essentially abandoned by her mother. Of course she is going to act out. I agree that counseling for both of you needs to be a priority.

I have a five year old and it is a tough age even without that history. How is she at school or with other adults? Do you use a sticker chart to earn rewards? Positive reinforcement is always better than negative reinforcement.

This is a lot to take on and I wish both of you the best.