We can't really tell you what she's thinking, but it sounds like you had a toxic parental figure that has created a rift between their children on purpose. It's common in abusive households to have the golden child adopt the abusive parent's mentality and see the scapegoat as the lesser.

Did you try talking to her about it? Sounds like you want a relationship, so maybe it it a try so you won't have any what-ifs. "I feel like you don't feel very close to me and I want to feel close to you. Was there something that I did that was hurtful to you? I want to make it right and I want us to be close and loving sisters." Or something to that effect.

But as you said, she doesn't owe you stuff even if you do stuff for her. You're assuming that she is trying to "take out" some sort of vendetta against you on your kid, but maybe she just doesn't want much to do with you and your family in general and it's about her boundaries, not trying to assert some sort of malice on you. If you feel out of place in a group chat, try building 1:1 relationships with them with invididual chats. If that falls flat, you know that you don't have much of a relationship with them. If you want to cut her off because she doesn't add much to your life and actively hurts it, that's valid. But make sure you're doing it in order to make yourself healthier and happier, not in order to try to make some sort of point at her. Do it for self protection and in pursuit of happiness, not in pursuit of manipulation.