@BlueOrange - heya stranger!
She's not going to change, not this decade anyw...
Wow! If she is textbook BPD, I"d be happy with the apology you got, however insincere it may or may not have been. She might be trying to be apologetic in her own way. She may be going through the motions because she feels like she has to apologize to maintain a family dynamic that is beneficial to her. Who knows?!
Back to your original question, which was whether she was being genuine or passive aggressive, maybe consider asking yourself questions about the possible answers, What if she was being passive aggressive, what then? How would that make you feel? What if she was being genuine, how would that make you feel? How would either intention or attitude change your relationship with her? The answers will tell you way more about yourself and how you relate to her than anything having to do with her directly.
The truth is, based on what you described, is that she has some serious issues (don't we all?). You might NEVER understand how she works, and it might not even benefit you to fully understand. It might be a much better use of your time and energy to try to understand YOU in the situation and develop stronger boundaries. Easier said than done. You will have to be creative in order to navigate the dynamics in a way where you are not allowing yourself to be disrespected without getting caught up in the emotions of the situation. It will be hard, but may be a better use of your energy to accept the situation for what it is and figure out how you can adapt to it in a way that shows you care and love about yourself.
I will tell you that, from my experience, BDPs do not like when people have boundaries or they can't get a rise out of someone. My close friend with BDP, realized that she couldn't manipulate me, so she stopped. She now tends to not gravitate towards me as much. I still love her, yet the distance is fine with me.
With family it's especially hard. It sounds like you love her very much, or you would not put so much into trying to make things right with her. But just because someone is your sister, doesn't mean they are any different than any other person. And people often suck. My mom, for example, I've come to accept that if I look at her and expect her to be what most people think of when they think of a "normal" mom, I get very upset, because that is definitely not her. But I remind myself that I am an adult now, so I don't really NEED a mom for my own survival and well-being. I have had to do a lot of "self-mothering" on my own. But when I look at my mom as a "person" in my life, I think, "Wow! She is pretty cool." I've actually learned a lot from her and she is very loving and forgiving, more so than anyone I know. When I think of her in that way, and dismiss her from the mom role, I really look at her differently.
Similarly, maybe its time to adjust how you view your sister. If she has such serious issues as you described, what is it that you can reasonably expect from her? Maybe a sincere apology is too much to ask. Maybe you will always have to be the "better person" or no one will. (Although I'm sure she's good at making herself appear to be the better person). How can you let her be what she is, but still remain in a place where you feel empowered and that you protect yourself with love and respect? The love and respect is ultimately from within yourself, rather than from external sources.