Think of it this way if it helps... your mother is ill. She clearly has issues that she does not deal with in a healthy manner, as violence in such a situation clearly indicates. If you truly don't want him to take action, when you tell your father, maybe not only ask for him not to do something arrest, but also ask about using this as a catalyst to get her help, even if it means holding the assault over her head. Ie: If she drinks, make not filing charges conditional on rehab. If it's an anger problem, anger management, and so forth.
(Though honestly, if it is just a case of shear narcissism, then be careful about going down the treatment rabbit hole. Use your judgement.)