Is it considered a sin for a daughter to confide in her mother about what troubles her from others, knowing that the mother will then backbite those people?

You are permitted to respond to abuse in kind, within the limits allowed by Islamic law, though forgiveness is superior. However, it is not permissible to retaliate with something that is not of the same nature as the aggression, such as lying, or declaring someone an infidel (takfir), or insulting one's father if he was not the aggressor. This retribution is a right solely for the victim of the aggression. Your mother is not permitted to backbite those who wronged you. If you know that she will backbite them, then do not tell her what happened, so that you do not burden her with committing a sin.