Hello, banabrea!

Please allow me to welcome you to the discussion forums. I'm so sorry for what you're going through but glad you have found a community where many of us have been through similar experiences, and we can learn from each other. I believe that you have found the best place in the world for understanding, compassion, and education as it relates to BPD, or facing emotionally intense relationships (as the byline of our logo says). So…we support each other here. I was a little scared when I joined, but mostly about having my fears confirmed. Now that they have been, I'm feeling much better.

So, again, welcome!
Thank you for sharing with us what you have thus far:
How do I broach the subject of switching to a therapist who has experience with treating BPD?
That's a toughie! I can appreciate your reticence in tackling this question with you sister. One way is to validate her ("I see that you've been having a hard time, sis.", and then to simply ask her if she'd be interested in trying a new/different mode of therapy, and see what she says. Another way is to have your parents do this. Either way, it's going to be up to your sister to embrace the process of DBT.
I know you are here by way of sorrow, but I just want you to know that you are among peers, friend. Unfortunately, there are legions of us! I'm so sorry you and your parents are experiencing this. However, I think you'll find a lot of parallels here - lots of members (including me) have similar stories. You will see from reading the posts here that you are far from alone.
There are also site articles and helpful tools that can be utilized by you to help you navigate this strained relationship. The tools are for YOU, but in time, hopefully, they will assist in improving your overall relationship with your sister.
It may also be helpful for your parents to visit this site, in order for them to gain a deeper understanding of what they've been dealing with at home as well.
I believe you will be greatly comforted by the support here and the fact that we really understand what you are going through. We've all been there to varying degrees. Take care of yourself. We will look out for future posts from you.
Keep writing, keep processing, keep learning!
-Speck