Are you able to be accountability partners for each other? (to stay in the coaching lane)
How would things change if he were able to accept BPD? Would it even be wise for him to accept it without a formal diagnosis?
Are these other family members diagnosed?
(Oops, I was trying to quote from multiple people and deleted what you quoted ... not sure if I can roll back those edits)
If he accepted she had BPD then he might understand some of the counter-intuitive skills that impact her safety. Like helping her develop better skills to communicate her distress rather than implying she is suicidal.
H works in health care and understands how the sausage is made when it comes to diagnoses. We both have research backgrounds and understand what the DSM is. And dancing around it hasn't made a difference in what I suggest (e.g. safety plan, DBT).
For me, acknowledging that she has the same traits as her mom (minus the raging) means getting off the roller coaster, for her sake and his.