This makes perfect sense! I am an only child, so no sister, but what you have described perfectly describes my mother - to the tee!
For the first time i realize what the problem is in the relationship. It is my reaction.
Ah yes. You are wise Ewemadame. Once we realize we are also part of the problem (it's not ALL the BPD's "fault"), we can learn new and better ways of interacting which don't contribute to the problem. There are lots of "tools" on this here board to that end. They all work. For me, the trick was/is to learn and reflect as we practice these tools, and also figure out which tool is best for each situation. I like to think that if a tool isn't working the way we want it to, we're probably not using it quite right.
I have set my boundaries firmly by letting her know I care and love her as a sister but will not allow her to speak so negatively and make false accusations about me and then the next day act as though none of it has happened and want to bring me cookies.
It still shocks me (1 1/2 yrs since I've been on this board) when someone describes their situation, and it fits mine like Cinderella's slipper. Except my mom always brought me homemade buns instead of cookies. My late father always called this mom's peace offering. It meant that mom had swept the incident under the carpet, moved on, and no one was to mention it again. Whether the rest of us had moved on was not important.

You do know those false accusations are not really about you...but about her? If you think about it, do those false accusations do a better job of describing her than you?
The torrent has begun. I have had to block her texts and emails. But I feel so much better and relieved. Does this make sense?
Perfect sense

Congratulations for taking the first step of setting your boundary, and then blocking the torrent. Stay strong. It's a process.
