How much do you know about borderline personality disorder? It's not at all uncommon for someone with the disorder to split. In my experience, with my family, if you aren't their hero, you are either out to get them, or they just shut you out. Since I don't engage in the drama anymore, I am not a part of the family (according to them). And since he's dredging up his past, past wounds and traumas, his emotions are probably churning around, and he's likely thinking less logically than before.
And no, it's not at all uncommon to absorb new friends' personality. BPDs have a fragile sense of self, and struggle with feeling any self worth. This is very common. Those suffering from the disorder often fuse psychologically with others, sometimes to the point of being emotionally unable to distinguish between their identity and that of a partner, or friend.
I suggest you don't push it. I know it's probably confusing to your daughter, but if he is around her while he is going through this "self discovery" (I like that!), and if there are arguments in the household, it could be hurtful to her. Focusing on her at this time is very important, in my opinion.
I can understand having anxiety in a relationship with someone with this disorder. Being raised by one, and having a sister with it, I have struggled with anxiety most of my life. It's important to pinpoint your triggers for anxiety. Mine flares up when I am around my family for more than a couple of days at a time, then can spin out to other areas of my life. If I don't recognise it, and catch it in time. Constantly worrying about someone - trying to figure out ways to help them, reassure them, dreading the next dramatic interlude, or simply trying to keep the peace in the family can trigger it for me.
When I was enmeshed in the lives of those family members, I isolated myself. I'm not sure if it's the same for you, but I didn't have the mental or physical energy to sustain other relationships. And being focused on them, I kind of absorbed their way of thinking. I didn't trust people, I got paranoid. I raged. That was my FOO status quo. Since I have unentangled myself, I don't do that, and have developed healthier, nurturing relationships, with myself and others.