What should I do with my mother who constantly mistreats my father, and should I agree with her actions to avoid her anger, taking into account the saying of the Prophet, peace and blessings be upon him: "Your mother, then your mother, then your mother, then your father"?

You are not permitted to help your mother abuse or harm your father. Rather, your duty is to gently and courteously forbid her from doing so. A son must enjoin his parents to do good and forbid them from doing wrong, without violence or abuse. It is not permissible to abandon one's mother completely. Rather, one must deal with her with wisdom and diplomacy, and seek the help of sensible relatives or righteous people to advise her. Parents hold a great status, so a child should not abandon them. Instead, he should gently advise them and guide them towards good, even if they strive to make him associate partners with Allah. He should accompany them in this world with kindness and supplicate to Allah for their guidance.