Is the questioner sinful because his mother does not wear the hijab, and should he compel her to wear it, and is a man compelled if his parents are divorced?

You must continue to advise your mother gently, kindly, and courteously to wear the hijab (definition). Know that if you fulfill your duty of advising, there is no sin upon you, for Allah Almighty says: "And no bearer of burdens will bear the burden of another" (Fatir:18). It is not permissible for you to compel her to wear the hijab. As for a man being disliked if his parents are divorced, this is incorrect, as many people live away from their parents and still enjoy the respect and appreciation of others.