Hello and welcome to the group

Sounds like your D26 might be in a transitional stage of having some stumbles as she learns how to be an adult, which is pretty normal. And, even adults without BPD may have some resistance to seeing a doctor, for a variety of reasons (my non-BPD husband included!). I say that not to minimize the hurt and challenges of your situation, where you love your D26 beyond words and only want her to be well. It's more to bring you some hope and freedom -- what you're doing (offering some info on other doctors, reminding her she can reach out to you for support, then backing off) is sensible and you're allowed to step back from managing her life.
I sometimes wonder if pwBPD have extra-extra-long "return to baseline" times. If I fell out with my doctor, then depending on what had happened, I might be able to "return to baseline" in a few days, maybe a few weeks, before being ready to look for a new one. If your D26 suffers from BPD, though, then she could be extra sensitive to situations like that, and take a much longer time (weeks? months?) to get to a solid
WiseMind baseline than other folks. It may well have been "too soon" for her to start to look for a new doctor -- she may have been telling the truth when she said she didn't want to think about it.
Seems like what you're doing is smart (reminding her she gets to choose, then backing away) and may actually benefit your relationship with her, as it gives all of you time to cool off and not continue a conflict.
Is she still on your insurance? Living with you?
Looking forward to hearing more from you, whenever works best for you;
kells76