Hi FigureIt,
your "how to" question would be an excellent question for the staying board

. Seriously, you are de-facto staying and the staying board is a good place to get support for managing the daily life in a staying situation. Does not mean commit yourself to staying, just means committed to using tools to manage a stressed situation. Exact what you asked for

I have to stay with my uBPDbf now and I'm trying to make the best of it. He feels that he comes 3rd in our relationship after myself and my D9. He believes he should be 1B in rank. Now when it comes to him I come about 4th and my daughter maybe 5th. His rank is himself, himself, his kids if they need or want something, then maybe me if it fits and maybe my daughter.
I will admit that yes I am a mom and I do spend time with my daughter. I do not exclude my bf, he chooses not to join. I have always given him an open invite to join me at her sports games, concerts, etc. he chooses to stay home, rock in his chair and watch tv.
Last night, he begins to "complain" how I'm never home and he's not important, etc. I just spent a month planning his surprise birthday party and having it, but he's not important.
How do I handle, respond to this without justifying that a 9 year old should have my attention?
that is a typical situation. PwBPD is struggling to manage own negative emotions. You are absolutely right that JADE is not the way to go - no need to get defensive.
The problem can't be solved - the situation will bring these emotions up again and again. If it comes too often and it becomes complaining for the sake of seeking a fight - boundaries - find a way to leave. To sooth the situation however you may use validation and SET. The key is to verbalize his negative emotions how he perceives them in his own mind without judging them.
S: I hear,
E/validation: you are truly not getting enough attention. Everyone else has higher priority and you come last.
T: The kids come first. The hard fact of life is that the remaining time is limited.
You can't fix his need for attention but you can acknowledge that it is causing him great pain. You personally may feel like an adult that he should not feel so distressed about it but well, that is BPD - unreasonable emotional needs that when unfulfilled cause trouble. Can't fill the hole but he may be able for some time when validated.