Hello and a warm

Age 13 is challenging already, and then to layer possible BPD on top of that... I think anyone would feel exhausted, overwhelmed, and at a loss. Like your post title says, it's already been a long road, and you know there's still a lot of the journey left.
No one seems to understand and even the therapists outside of that one psychiatrist just brush off the potential of emerging BPD, stating she's way too young and I never should have been told that.
Touching on this first, I think there is a change at the forefront of research to understanding that it's not like some switch gets flipped, and at age 17 years 364 days "your child does not have BPD, she's just a teenager" but at age 18 years 0 days "oh yeah, that's definitely BPD".
Dr. Blaise Aguierre, who I believe is affiliated with McLean Hospital, wrote
Borderline Personality Disorder in Adolescents and suggests that yes, BPD is diagnosable in teens and can be differentiated from "typical teen" behavior and from other psychiatric challenges. Not sure if you've had a chance to look at it yet -- could be a helpful resource.
McLean Hospital has a
treatment center focused on teens with BPD (or teens without BPD who could benefit from DBT). So, they too see BPD as possible in adolescents.
All that to say -- whatever the "label" for what your precious daughter is going through, BPD is a possibility at that age, and I feel you on wanting to get her real, effective help, so that instead of a life of struggle and pain, she can enjoy peace and strong relationships

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Another good resource for families where a member has BPD is the
National Education Alliance for Borderline Personality Disorder's free program called
Family Connections™ - BPD/Emotion Dysregulation. I took it last year (briefly, my husband's kids' mom has many traits of BPD) and found it helpful, clinically up to date, and supportive. There is typically a waitlist (I believe I waited ~7 months) so it could be worth signing up now. You can always opt out later if life changes.
The group I was in did include parents as well, and many parents were in a similar position -- loving their children, having compassion for their children, but needing to find new ways to parent and support their children.
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Just a few questions to get a bigger picture:
Is your D13 generally compliant with going to treatment? What I mean is -- sure, she might verbally say "I hate this, I don't want to go, you're ruining my life", but fundamentally does she go? Doesn't try to run away, leave the office/facility, etc?
Does she seem to want help with having better friendships/relationships?
Who else lives at home -- do you have a spouse/partner? Other children? How's the family doing?
Fill us in some more, anytime... we'll be here.