I think the main point is that the OP trusted her sister to stay out of the argument between the OP and her mum. The sister broke that trust by getting involved, instead of letting the OP and her mum work things out among themselves.
TBH, it may not be the best thing for many, but if you base your relationships/friendships on trust, then if you find that you can't trust someone you thought you could, you need to move on with your life.
Life is full of regrets, the difference is whether you can live with those regrets or not. People are still people, no matter if they are related or not. Sometimes it's better for you and your own family to leave these people behind. Ask yourself this: What does your mum and sister bring to your life? If it's kindness, respect and decency, then you could possibly sort things out with them. BUT, if they bring nothing but drama, trouble and disrespect you, then you can choose to go LC/NC.
Don't get me wrong, I know it's hard, but it's hard because you've been conditioned to believe that your supposed to put your sister/mum/dad/brother's feelings before your own. Absolutely not. That way lies madness, and when a situation gets more and more out of control, you'll probably wonder why you didn't stop contact earlier.
I'm sick of all this whining and whinging about "Oh, but he's/she's your sister/brother/dad/mum, and they're family". Fuck that, for a game of soldiers. What I've learnt about families is that in some situations your friends act more like your family than your siblings/parents do. If your friends treat you better than your family do, stick with your friends.
I have a similar situation with my family. My older brother stays out of things between me and my other siblings/mum. My younger brother, however, interferes in everything and made issues between mum and myself so much worse. To the point where my mum called me a bitch, a prick and an idiot. Sorry folks, but my mum burnt her fucking bridges when she did that. It's not even what she called me, it's the fact that she said it to my son, and dragged him into issues that were nothing to do with him.
It took DS 7 months to tell us this, as he was afraid of how I'd react. I just rolled my eyes as I wasn't in the least bit surprised. Mum is the type of person that is very nice and charming to the outside world, but is a nasty piece of work and always has been to me.
The reason my older brother stays out of things is because he has had his eyes opened as to what mum has been like to DH, our DC and me. I took the opportunity to move away and wasn't going to tell anyone except close friends. Unfortunately I gave my older DB my new address, but had I know that he would give it to my mum, it would never have been given to him.
Thankfully I'm now over 400 miles away from my home town, where the rest of my DB's SIL's and mum live. So there's not much chance of a visit from my mum as she's very frail and could pass away at any time. After what she put me through as a child and adult, I can't even muster up the will to even fake any upset over her death.
Call me a cold-hearted bitch for that if you want, but I have plenty of empathy and sympathy, which is only reserved for those who have treated me with kindness and respect over the decades.