How should I deal with my father who abused my mother in the past and caused her illness, but has now changed for the better? And is treating him harshly considered weakness and baseness?

You must be dutiful to your father and treat him with kindness. It is not permissible for you to mistreat him or deal with him harshly, as that is a forbidden act of disobedience (uquq) and one of the gravest sins. The right of a parent over his child does not fall away due to his injustice or his falling into sins. His mistreatment of your mother is not a justification for mistreating him, especially if he had repented from that mistreatment in her final days.

Your mother has passed on to her Lord, and your harshness towards your father will not benefit her. Rather, what will benefit her is your supplication for her and your charity on her behalf. So, be keen on being dutiful to your father, for the Messenger of Allah, peace and blessings be upon him, said: "The father is the middle gate of Paradise; so if you wish, neglect this gate or preserve it."