You are between a rock and a hard place. On the one hand, listing your mom and her educational status may help explain your situation as a first generation college student. And you feel that your father's abusive behavior is an important part of your "why medicine" essay. If you are going to list only your mother's name on the application, which some people do if they were adopted or didn't otherwise have a father, but write about your father and not list him in the parent section, as if he didn't exist, it will raise a question. Of course, writing as you plan to about your father and then listing his name can raise eyebrows, too.
And, btw, on the AMCAS, parents can be listed whether living or not and there is a yes/no question about that status.
Frankly, I'd recommend a a long look at your personal statement and see if there isn't another approach to the "why medicine" essay that does not include your relationship with your father.