My SO's Daughter's also refuse to see their uBPDmother. D19 only communicates via email. D15 still talks to her mom on the phone. If your daughters are like my boyfriend's daughters they probably have been through a lot because of their mother.
Some of the highlights in our situation have been uBPDmom failing to get daughter dental care (back when she had primary custody) so daughter had tooth pain for months, filthy house, dog feces in the livingroom, evicted 3 times (daughters came home from school to find there possessions on the lawn) those same possessions were put in storage not paid for so auctioned off, used as babysitters and maids while when mom couch surfed at the homes of friends and relatives (between evictions), but the icing on the cake was to send older daughter to college and pay for it with "the family trust" only there was none so D19 is now 15k in debt for a semester of school that she can't get the records for because she can't pay and finally uBPDmom sent younger daughter to camp out of state only she didn't pay for it so D15 was stranded with a friend of her mothers that she didn't know for several days with no way home (she was also instructed to not tell her dad where she was), mom had no way to pay for camp and we also found out that she didn't pay for camp the summer before. These stories of neglect don't even touch on the emotional abuse, the parental alienation (that went on during the divorce), the FOG, and the playing one daughter off the other one.
I tell you this just to point out the obvious that these kids have been abused in so many different ways that they cut off the abusive parent because they can't take it anymore only to feel the guilt of cutting them off, and the vain hope that parent will change. It is a horrible place to be, trapped in the middle of hope your mom will be the mom you want her to be and the reality that she is abusive.
My SO's younger daughter at 13 made suicidal threats to her school and was briefly admmited to an inpt psych facility. While there she was diagnosed with PTSD. She also has received skills to cope with anxiety, is on medication, and has a therapist now that gets mom is the problem and is helping D15 work through the issues surrounding her mom (her therapist prior to admission bought what BPDmom was selling and had trouble enforcing her boundaries with uBPDmom this did not create a safe place for either daughter to talk).
None of us here can diagnose anyone but I encourage you to read about PTSD see if it seems to fit (her extreme reaction to possibly seeing her mom is a

to me) and tell your daughter's therapist your concerns. I think your daughters therapist is focusing on some good things by trying to get the the self-harm and anxiety under control but if you talk with the therapist and going forward you still feel the therapist is ineffective you might consider looking for someone else (do keep your daughter's feelings in mind here though she might trust the therapist and not feel comfortable with a change).
I also want to ask if you are receiving therapy? You have a lot on your plate just simply by being the dad of 4 kids! Then throw in a BPDx the stress and demands are escalated. My SO received therapy shortly after his divorce that helped him with strategies to help his kids (or at least do no harm). I encourage you to reach out for help if you haven't already.
You are obviously a concerned and caring dad doing his best. Trust your gut and keep being an advocate for your kids. (Don't forget to take care of you too... .self care is key)
Take Care
Panda39