It is possible that your sister has a deeper problem that others don’t see. If this is the case, your mother should consider seeking the help of a professional to help her deal with your sister. Remember that there are always two sides to a story, and that unbeknownst to your mother or you, other things may be going on in your sister’s life, e.g., private challenges.
In sum, try to be dan lekaf zechus by speaking with your mother privately – when both of you are relaxed and in a good mood. If you speak about this when one or both are angry and/or frustrated, a fight will likely ensue. That, of course, will be counterproductive to what you are attempting to accomplish. Hatzlachah!