There could be a reason for such behaviuor, ie. depression which could be easily treated with drugs ? All human behaviuor could be explained and improved with counseling, communications and probably interventions if the situation does not terminate.

One good rule to have is to listen a lot: listen to your mother, listen to your sister. It sounds like you may be right, that your mother's depression is affecting how she relates to your sister. That's sad, but it's a fact that depression does tend to distort one's relationships. How is your sister responding to this? Is it upsetting her? Do you think she can understand that mum's depression is the source of the problem? Another good thing to do is to avoid judgments: try to restrain the urge to blame your mother harshly -- if she's depressed, she's in pain, and this is one of her ways (not a good way, of course) of expressing her pain. It's possible to have compassion for her pain while simultaneously trying to help her find better ways of relating to it. Will your mother accept any help? If she's really depressed, therapy and/or medication can be helpful. Is that a possibility? In many areas, low cost treatment is available if you do some research. In the end, your last 4 words are probably the best thing to hold on to: keep asking "how can I help?". Keep trying to be alert, observe the situation, and look for ways to help.