Hi usagi;
Good to hear that even though your partner has some big stuff on her plate (new job, not feeling like she wants to do therapy), she is still willing to go. That takes a lot and may be what doing her very best looks like.
Overall my thought is to pump the brakes for yourself a little and focus on sitting with your discomfort.
Even for "generally normal" persons, therapy is not a short process. I've shared elsewhere on this board that I've been seeing my individual T for a couple of years now, and there are still areas where I'm not totally transparent with her. It's hard. I have insight and awareness that there are some doors I'm keeping pretty tightly closed, that impact my current relationship, but even with that insight there is still a big gulf between knowing and changing... and that isn't something you can rush or "just white-knuckle yourself there with willpower".
It is common for couples T's to meet with each partner individually as well as together. You can consider respecting your partner's wishes that the BPD label not be used, by not using it in joint sessions. In a sense, she's right -- the issue isn't the label, it's behaviors and dynamics. If it were me, and after a couple of joint sessions I checked in with myself and found that it remained important for me to bring up, I'd do it in a solo session with the T.
If the T doesn't offer individual check-ins, it would seem pretty normal to request one (with the offer open for your partner to do an individual check in as well).
Give yourselves some time to get to know the T, get familiar/comfortable with the session dynamic together, and maybe find some "quick wins" that build common ground between you and your partner. Like you mentioned here:
I told her that I wanted to open by talking about all the things that keep us together. Our connection, shared interests, caring for each other and the like. My partner has decided that communication is an important aspect of improving our relationship. I agree with that and am hopeful that she's willing to try to see how her communication leads to problems. She's said that she doesn't necessarily want to focus on the past but realizes that talking about some of the big moments from the past year is probably needed.
that seems like a good starting point.
My guess is that you really, really want to solve and fix things as quickly as possible... That's
your feeling to manage. Letting it drive your choices means you might not be in
WiseMind -- you might be letting your fears/feelings drive the speed of the process. Trying to speed up a therapeutic process won't make it work better.
My thought is to notice your fear and discomfort and practice tolerating it.
Everything will not be solved or said or aired or agreed on in the first session. This may be uncomfortable, anxiety-inducing, etc. Can you live with it, and be patient?
For couples T to have some shot at success, both parties need to buy into the process and feel like the T is an ally. This may take longer for your partner than for you. Can you be OK with that?
Lots of questions... curious if there's anything to bounce some thoughts off of there?