My dad died 6 months or so after I was shunned. Of course, he pre-shunned like the extreme JW he always was. I remember my mom researching BPD to try to figure him out. It never fully fit as a diagnosis, but in the end it doesn't matter the label, he was who he was. When he died I grieved not the loss of the father I had, but the loss of the father I never had, and honestly my life didn't change for the worse because he was gone. I honestly let go of him when he shunned me. I was dead to him, he was dead to me, same with the rest of my family. I'm not going to sit around pining for people that actively shun me. I mourned their death with my shunning. If they come out someday then it will be like the resurrection I was promised. If they don't, that's on them.
I'm sorry that you lost your sister, and that with that you lost opportunity. I'm sorry that she was such an awful person to be around. However let me say, in response to......
I have ALWAYS held out hope that she and I would at some point reconnect - I have wanted that desperately. Every major life event that happened to me, I'd send her an invitation (never got a response). The only thing I wanted was to have my sister be my best friend...that's it.
Acceptance means letting go of the hope that it could have been any different. Read that again. Now once more and compare that definition of acceptance to what you wrote above.
Your sister was hurt in some way, thus the BPD. She was doing her best, and sadly her best was pretty awful. My dad's was too. In learning more about my dad's past though I get it. He was the byproduct of terrible parents that drank and threatened each other with guns and put him in the middle of a bitter divorce that split him from his siblings, who as the oldest he felt responsibility for. He was a very hurt person, and hurt people, hurt people.
That doesn't mean that the hurt he caused me doesn't hurt, but I can't hold someone to the fire for doing the best they could with the tools, or lack thereof, that they had. I had to let go of the hope that it could have been different because it couldn't. The same is true with your sister. She was likely doing the best she could with the pain and dysfunction that she carried and that others played into. People with BPD change the people around them too. It impacts others who then act in a reactionary way. It's like an addict and how they make everyone around them sick and often codependent.
If you want to love her then you have to love her for who she was, balance the awful treatment you received with the understanding of who she was and what she herself was up against, and let her go. Maybe write a eulogy you'd give and even if you never give it, get those feelings out and find some closure. Say goodbye to the reality of who she was and who you wished she could be with the acknowledgement that she was likely doing her best. Most people, even awful people, aren't malicious, they're just messed up, broken in some way, taking that brokenness with them everywhere they go and impacting others because they either haven't got help or there's no help for them. For many with BPD they will never get help and honestly the disorder itself precludes them from doing so. It's awful, and she wasn't happy either. A very tortured soul.
Take care of yourself, hugs to you, and I hope that you can find some acceptance in your life. It's one of the stages of grief, the one you want to get to, but also remember the grief isn't a linear process. It's messy. And it's not something you may just go through once and it's done. You take grief with you through life, but you get better at managing it. Let go of the hope that this could have been different. Everyone was likely doing their best, even if it wasn't good enough.