Salam - Struggling with my father's behavior and protecting my mother

Salam. I (22M) am really upset and furious with my father. My sister (14F) found a video on his phone of a non-mahram woman dancing in revealing clothes at an event. She told our mother first, then me. We were all disgusted and our mother felt deeply betrayed. When I confronted him he kept denying it and called my accusation false, even though I have the evidence. I reminded him to fear Allah, and now I find it hard to even look at him or want to speak to him. My father has been abusive toward my mother for a long time - I could write a lot about the harm he’s caused her. He says terrible curses to her, using filthy language no husband should use. Seeing her cry so often breaks my heart; she deserves peace and happiness. That builds a lot of anger in me toward my father. My mother wants to move out and possibly pursue a divorce. We can’t tolerate this situation any longer. I will be moving with her and will take the lead on financial responsibility. My priority is to make her feel safe and at ease - something my father has failed to do. Am I sinful if I completely cut off ties with my father? I know Islam commands kindness to parents, but an abusive person seems undeserving of respect. EDIT: I also should say my father’s practice of deen has collapsed - he abandoned salah, stopped engaging with the Qur’an, smokes often, routinely backbites about my mother’s family, and lies a lot.