This. In fact, to get a better perspective on the situation, take this out of the equation.
Imagine, that instead of being your sister, this was, say a co-worker who you’d worked with. Maybe she was like a team lead when you first joined your first project. And this co-worker was a pain in the ass, and never showed you any respect. But, since you both continued to work for the same company, your paths would cross from time to time. And try as you might, you never established any sort of friendly, mutually respectful relationship.
Then she is transferred to a branch in England. So you think she’s out of the picture, but she flies back every once in a while for company business. And when she does, she contacts other co-workers at your office, and that’s how you happen hear about it. But you’re always the last to know.
On one of her visits she hears about your family, and decides to “act” friendly and reaches out to you to see if you can get together so she can see your child.
The point is, if this were the case, that she was just an insensitive co-worker, you wouldn’t have any issues about severing any contact/relationship with her.
I feel that, even though she is your sister, you have no obligation to try to maintain any relationship with her given that she clearly doesn’t put any effort into having any relationship with you. I believe that at some point, you go from being a child to being a person. And when each of us reaches that point, we are now responsible for how we live. The circumstances of who we happen to be related to are less important than how we further nurture or discard relationships. It sounds like your sister has resented your mere presence from the day you were born (quite literally - she was a 4 year old center of the universe to your parents, and then YOU had the audacity to shift your parents’ attentions away from her !). And she has chosen never to build upon the fact that you are related and have a reasonable relationship.
You, too, have this option. You may get a lot of criticism from the “blood is thicker than water” types, but the fact is, you just happen to be related and only have control over how you live your life. Feeling guilty that she is your sister, but you’re severing ties comes from the belief that you are somehow obligated to love/care, etc. for your sister NO MATTER HOW SHE TREATS YOU. And I disagree.
Once you become “persons”, you (both) now choose with whom, and what kind of relationships you will have - even with siblings. With siblings you may have a “head start” in that you’ve known them your entire life, but there is no inherent obligation to continue a relationship if it is not a healthy one (IMO).
It’s certainly your choice to keep trying to establish a relationship with her. But don’t beat yourself up if she doesn’t reciprocate. And when you feel you’ve put in “sufficient” effort and she still treats you poorly, then give up trying (and don’t feel guilty about stopping).