My mother treats my father very badly, so what should I do?

You must be good and righteous to your parents, and it is not permissible for you to fall short in their rights, no matter how much they may fall short in their rights towards each other or towards you. The rights of parents are great, and Allah has associated them with His worship: "Worship Allah and associate nothing with Him, and to parents do good," and "And your Lord has decreed that you worship none but Him, and to parents, good treatment."

And the right of the husband over his wife is great, so the Muslim woman must obey her husband in what is good.

As part of your complete righteousness to your mother, you should advise her calmly and gently that her treatment of her husband is not permissible in Sharia. If she responds, then that is well and good. Otherwise, it is not permissible for you to hurt her feelings or harm her. Rather, be good to her, for "And no soul earns [anything] except for itself, and no bearer of burdens will bear the burden of another."