It is difficult to have a parent's rights terminated.
What you describe could be considered neglect. If CPS were to look into the situation it may provide some help for your sister. However, CPS tries to keep families intact and the child does not always get removed from the home.
Perhaps you can get your mother to consider giving you temporary guardianship and take it from there. That doesn't seem as drastic of a step and your mother may allow it.

