How can I be God-fearing in my dealings with my mother and show her righteousness, despite her harshness and her causing me psychological distress and disagreements? And what is the way to help myself show her righteousness?

If what you mentioned about your mother's harshness is true, then you must supplicate for her righteousness, and be patient with her harm while frequently remembering Allah, for indeed, the remembrance of Allah removes worry and brings happiness. You have done well in honoring her, for parents are to be honored and treated kindly no matter how much they err, even if they are disbelievers who enjoin polytheism, as evidenced by the Almighty's saying: "But if they endeavor to make you associate with Me that of which you have no knowledge, do not obey them but accompany them in [this] world with appropriate kindness" [Luqman:15]. Honoring one's parents includes every good deed that can be offered to them, including supplication. Strive yourself in honoring her, for striving makes difficulties easy. If you find someone among her relatives or friends who can advise her kindly, then seek their help.