changingtimes,
So good to hear your DD is in therapy. You absolutely should mention your concerns to her therapist. I would not specifically mention BPD but the behaviors. Mention that you would like her therapist to start gradually working on her relationship with her Dad.
I think making it clear that you are just as confused by your ex's behavior as she is might help to ease the pressure you feel to explain things.
I would probably try to let her therapist do the work first. You have enough on your plate sounds like! My DD were both in therapy for a few years and are emotionally very mature.
I am also a step mom. I remarried to a Non. My 3 SS are now 8, 10, 15... . they are still more emotionally fragile like your DD and I could never discuss their mother's illness head on. We say things like
"oh you know mom! She is bad at making plans,"
"mom gets kind of emotional sometimes"
All 3 are in therapy.
My SS do also live with us 90% of the time now, but do spend a few intense weeks of the summer now with BPDbioMOM in another state and they always come back an emotional mess.
As for your DD13 developing BPD herself, well keep an eye on it. Some of it is what we call

fleas from learning coping skills from a BPD parent.
I also post a lot over on the Supporting a Son or Daughter Board... . because my SS10 is so much like his BPD bio mom... . but too young to get any kind of BPD diagnosis.
A couple great books to get yesterday

are:
I don't have to make everything all better by the Lundbergs
as well as
Essential Family GuideHope this helps some. Others may have good ideas for you as well.
Welcome to bpdfamily.com and keep reading and posting. You are definitely not alone!
Yours,
mamachelle