OP don't beat yourself up about it. I guarantee your sister isn't doing the same. Whatever you did would have been wrong. Because to fix this relationship needed both of you to want it. And your sister doesn't. Not for now anyway.
You had the best intentions and anyone who judges you doesn't know a) the truth of the situation or b) the real YOU.
I recognise your relationship because it sounds like my own with my younger sister. She has hurt/rejected me so many times and all I have wanted was to have a better relationship
. I think that although it still hurts (when she doesn't want to see me, her neice nephew etc at xmas and arranges secretly to see my parents but doesn't invite me), I just take comfort from the fact that I've tried and have my own little family unit. I grieve what I don't have, a sister, an Aunt for my children and parents who are interested in and part of their grandchildren's (my children) lives.
But I have found some inner peace about it on the whole. I've stopped trying to understand why and tried to accept that people have their flaws. It's her problem, not mine and I can't do anything to change it/her/them.
Your sister will have her reasons for her behaviour towards you, but it's complicated.
She probably doesn't understand/acknowledge her real motives herself, or want to. I suspect she took her self worth from your "black sheep" status, which made her feel superior, felt angry with you for what you put your family through in your turbulent early years and deep down doesn't forgive you for that.
You can't change that, however much time passes and however much you have changed. It's how she still sees you. And that's sad and unfair but out of your control.
Unless you have family therapy or she has an equal desire to mend things, I don't think you will ever have the relationship that you want with your sister. It's not in your power, so let go and take control of what you do have the power to change from within.
Don't give her the power to hurt you by putting yourself in vulnerable positions. But do hold your head high that you have tried and actually considering her long term behaviour towards you, that's very commendable. You have nothing to be ashamed of.
You need to find a way of making peace with not having the sister you want but not alienate yourself from your family and friends.
It's very raw and painful right now but no real harm done. Don't torture yourself by imagining what games she is playing or what people will think. She's not a very kind or decent person if she feels the need to do that.
You know your truth OP. Be strong. You are a better person, remember that.