How should I act regarding my sister's request for me to tell her what Mother says about her, knowing of their disagreements, and would I be considered a backbiter or a liar in either case?

Kindness to one's mother is an obligation, and quarreling with her is an act of disobedience (uquq) and a major sin. It is not permissible for a sister to tell her sister what their mother says about her, because this is forbidden backbiting (namimah) and a major sin. If her sister asks her, she should not tell her; rather, she should ask her to desist from this question, and she is permitted to lie to avert problems.