Look into the four major personality types, which are (and have many different names, but here are the ones I use): Persuader, Authoritarian, Analytical, and Peacekeeper. These come from two measures: whether a person is focussed on other people before themselves (affiliative) and whether they naturally dominate others or not. Here's the breakdown:
Affiliative, Dominant = Persuader
Non-affiliative, Dominant = Authoritarian
Affiliative, Passive = Peacekeeper
Non-affiliative, Passive = Analytical
There is a good chance your mother is like mine -- Authoritarian. You are probably like me, an analytical. Your sister is probably Persuader or Authoritarian, like your mother. Your mother respects dominance. She considers it courage. Those who do not dominate are cowards. Therefore, they do not respect them.
I'm in the same exact situation -- my brother, a Persuader, can do anything, say anything, no matter how amazingly over the top, and my Mother, an Authoritarian, will not say anything. If I stand up for myself in any way, no matter how small, she pounces with nuclear force. It's natural -- she's not thinking, she's feeling and being primitive and is a slave to her brain. All I can do is ignore it -- and I think it is probably the only thing you can do too. Take control of your kid because that kid is yours and just ignore the outbursts. She'll go... nuclear. She'll RESPECT YOU more, however.