Hi Wilkinson!
Every situation is different. Every relationship. Every person. That said, as someone who was ready to leave who then decided to stay, I'll give you a little bit of my experience.
My uBPDh had already shown some minor

but last year things got really bad. Verbal and emotional abuse on a regular basis. Taking advice from people here, I started seeing a domestic violence counselor.
One weekend while he was away, things came to a head and I told him I was going to move out.
It terrified and shocked him. He said he'd had no idea it was so bad. He was already in anger management therapy (he still has no idea about BPD) but he really knuckled down. He genuinely apologized and took responsibility for his behavior -- still does. He didn't remember a lot of what he'd said and done, but he didn't doubt my account. With his work and the tools I've learned here, our relationship has greatly improved.
It is possible for things to improve and change. But something my therapist stressed to me was the importance of "real change." There are some signs and one of the big ones is a true willingness to accept responsibility. It sounds to me like your wife is minimizing, making excuses, etc. Those are

and are common in abusers who are just trying to keep their partner around.
Here's a list developed by Lundy Bancroft, who's something of an expert in domestic abuse. This is about abusive men, but if you switch the pronouns, it still works:
Admitting fully to what he has done
Stopping excuses
Stopping all blaming of her
Making amends
Accepting responsibility (recognizing that abuse is a choice)
Identifying patterns of controlling behavior, admitting their wrongness
Identifying the attitudes that drive his abuse
Accepting that overcoming abusiveness will be a decades-long process, not declaring himself cured
Not starting to say, “so now it’s your turn to do your work”, not using change as a bargaining chip
Not demanding credit for improvements he has made
Not treating improvements as chips or vouchers to be spent on occasional acts of abuse (e.g. “I haven’t done anything like this in a long time, so why are you making such a big deal about it?”)
Developing respectful, kind, supportive behaviors
Carrying his weight
Sharing power
Changing how he is in highly heated conflicts
Changing how he responds to his partner’s (or former partner’s) anger and grievances
Changing his parenting
Changing his treatment of her as a parent
Changing his attitudes towards females in general
Accepting the consequences of his actions (including not feeling sorry for himself about those consequences, and not blaming her or the children for them)
So, in my opinion, you're right to be wary.
You're also right to not share BPD with her. That almost never goes well.
Have you spoken to a counselor of your own? If you feel firm in your decision to keep a separate home, then move ahead with your plans to set up a custody arrangement for the children. No, your wife won't like it and may make things difficult. (Our forum on Divorce, Co-Parenting, etc. will have a lot of good advice for you:
https://bpdfamily.com/message_board/index.php?board=10.0.) But you have to determine what's best for you and your children so decide that. Set your boundaries. Move toward your goals with wisdom and empathy.
I'm sorry. I know this is a difficult spot to be in.