Hello Parkfriend, and

Having a loved one diagnosed with a serious mental illness can be scary at first; on the other hand, having that diagnosis can also be the first step towards healing. Please know that, first off, you've joined a wonderful community of caring people who understand what you are experiencing. You are not alone.
It's true that some therapists are not well-equipped to deal with BPD. On the other hand, there are success stories for patients that find the right path and commit themselves to healing. You may have heard about Dialectical Behavior Therapy (DBT) at this point, but here is an additional resource with some excellent info on the subject:
The basic principles behind Dialectical Behavioral Therapy . Finding a therapist who specializes in this treatment could be the next step forward for you and your daughter.
You might also wish to check out
What can a parent do? and our
Parenting a son or daughter suffering from BPD board. There are plenty of parents on the board who can share their experiences in dealing with a child suffering from BPD, and they know exactly what you are going through.
Please keep posting, Parkfriend. We are here to help and support you!