Should you forgive your mother who has taken you for granted all your life?

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My mother just turned 66 years old and recently has become weak due to dehydration. She is an alcoholic, and has not taken any solid food for a week now. We live in separate houses, and despite our differences, seeing her in her weakest state when I visited her broke my heart. She lives alone, for my dad has left her for another woman. She could not co-exist with anyone, as she is an arrogant, self-righteous woman who thinks everyone around her is inferior. We grew apart because all she ever cared about was our father. She turned to drinking and smoking when our dad left her. Now, her vices are taking its toll on her, and she has no one to take care of her but me. I don't mind taking care of her, what I don't like is up to now she still does not care about me or any of my sisters. In fact, she even believes we owe her and that it's pay back time, hence, we shouldn't complain about taking care of her. I know it is only a matter of time and she will soon succumb to her illness, so I thought maybe I should let bygones be bygones. I feel sorry for her, but I don't see her feeling any remorse about how she treated us. I believe forgiveness is for those who are sorry, but she being my mother, I don't think I will have peace within if I keep on dwelling on her past mistakes. Should I forgive her?