I think you need to really look at this relationship and stop being so black and white about it. She is not a bad person because she disappoints you and she’s a brat. That’s just who she is. Accept it, and instead of thinking, I’ll just cut her off now, maybe just care MUCH less about what she does. Sisters or relatives doesn’t always mean you’re going to be close or even like each other. That’s a huge fallacy of life. You don’t have to let her life make you feel so low.
It really sounds from your other comments that you could do with focusing on yourself and building a community and network of friends that make you feel good.
I’m sorry about your dog.