@Floatyfox - I'm really sorry to hear this! I've experienced this too, for a number of years and it's deeply deeply painful. It is like a bereavement but one with zero support and blame and shame as illustrated by the pretty blunt replies here. You literally have to grieve for your sister as this may last a lifetime but there is no acknowledgement of grief, no support. Having spent a number of years feeling it, having no one to talk to as people are even harsher in RL so therefore thinking about it. These are my thoughts:
This is hard to hear but I believe that there's always parents behind it, not always intentially but you do mention standing up for your mum. In my case my mother slagged me off to my siblings for years. They used to tell me what she had said, it was painful. And they didn't seem interested in my point of view. So different to your situation. Also in my family because there was abuse growing up, we just had to take it. There was no practice in falling out with each other and more importantly making up! If we don't practice this, then how do we get to do it as adults? So, in my case there was all this silence about the past, strong feelings never expressed, so it just sort of came my way.
I wonder what it may be like to explore more complicated feelings for your parents. Even briefly to take the focus from your sister and turn it to them.
And do some grieving. It's painful. Grieve for the time she wasn't there for you. Start grieving for now too. I think it's tough when our siblings aren't there for us. But the fact is, they don't have to be. And they're not always going to be.
It's ok to fall out. Forgive yourself for anything you said, you're willing to make up. She isn't. It's deeply sad but you can't make her engage. I'm sorry she won't.
And start thinking about your choices. How much do you want her in your life right now? Do you want a Christmas card relationship? Are there other more fulfilling relationships in your life worthy of your energy?
The grieving doesn't end for me. But I've come to an acceptence. I wish this was better supported in society but it isn't. But to say, I very much get the pain. All the best.