first I want to say I feel for you, and my heart goes out to you. I know this is tough and no words can make that better for you

I will say that you've done more than your share with trying to reconcile with the people in question, and unfortunately the ball remains in their court. Should you give up? I can't say for sure, but I can say that for the moment letting it be is the best course of action. Does that mean that you just walk away forever? no. nothing is forever and things can and probably will change in the long run, for better or worse.

Thing is continuing to try to reconcile with the unwilling only will serve to make them have more assumed power over you, giving them more confidence to continue to berate you and make you feel small and wrong, etc. By letting it go and showing them essentially "ok, it (or your acceptance and repentance) isn't that important in the grand scheme of things is far more effective at sort of subtly knocking them down a notch or two. Part of the problem in this situation as I see it is the self importance that she places on herself. Don't let her continue to be "important" in your mind for now...

But you've got to realize yourself first that in the grand scheme of things, she isn't the end all, be all, sister/friend/etc.. but your life will go on and your success therein is independent of her approval and acceptance.