Kitkat90, this sounds like a very difficult situation.
There are a lot of positives to celebrate in your story. First, congratulations on your moving out and getting your own apartment. You are clearly a very kind person to take in your sister and nephew and to let her use/give her your car. The most positive thing in the story, is your self awareness that it was not working, setting a boundary and insisting she move out! And because of your boundary, she has made progress and is much more self sufficient. Double congratulations on that!
Unfortunately there's no way to get off their list, no convincing them or changing their minds. Unless they decide you've done something to get off it, you're stuck there.
Wools is right. She was in your home as a guest, and she invaded your privacy. You have been nothing but kind, and she is the one who was wrong. AND she will never acknowledge it. My sister wBPD will go to the grave with a laundry list of all the things I did to wrong her, many of which have some remote basis, but are mostly projections and distortions.
The other good news is that you have the space now to work on yourself, how you feel and how you react. When we are always “reacting” to the pwBPD, we are often suppressing our own feelings and don’t have the opportunity to heal. As you describe your childhood and journey, it sounds like you are taking many healthy steps towards healing, but be patient with yourself. It will take time. This forum and the readings Wools provided are a perfect start. Please keep posting and reading others posts. There is so much to learn about our selves through seeing we are not alone and learning and supporting others who are experiencing similar things.