It sounds like you are saying he sleeps in a separate bedroom from you, and sometimes he insists your daughter sleep in his bed with him.
Have you considered he could be abusing your daughter?
His alienating treatment of you and behavior towards the girls are classic red flags for suspicion of his sexual child abuse.
I do have some experience with BPD, but I wouldn’t even know where to start in explaining and it’s about my having emotional dysfunction tied to an extremely difficult dynamic with my husband. These things I described are parts of possibly having BPD.
But, I’m also really people smart and astute. I’m concerned for what you described involving your girls.