Thanks again Pook075 for your reply.
Everything you are saying makes sense.
The thing is, I've done all this before - cycling between periods of calm, followed by dysregulation, followed by me reaching out and helping my husband come back to stability. The thing is, something snapped in me after his last cycle and I just don't want to do these cycles anymore. I don't want to rescue him.
It's not because the relationship is unfair, I honestly can come to terms with the fact that his contributions may look a lot less than mine (e.g., taking care of kids, employment, household chores). I can even come to terms with the fact that he doesn't love me the same way as partners do in a healthy relationship, and it looks different because of his mental illness. I can come to terms with the fact that I am often very embarrassed by his behaviour and that he is unreliable. I can even handle the fact that I can't trust him (I'm not talking about cheating here - that I could not handle - I mean can't trust him to babysit or to be consistent or have a job etc.). I am happy to support him as he heals, even if it takes years. I am ok with living separately for years if that's what it takes, even if people think we are pretty strange for adopting this arrangement.
What I can't handle anymore is living like I am in a minefield, where an explosion can go off at any second and derail my stability. My psych just can't take it, and then I find myself not being able to talk care of our children and be there for them the way I want. It's too scary to live in a minefield. So yes, I know how to stop the current cycle - reach out to him and say the kind words you suggested - I have done this countless times before. I just don't want to anymore. Not because it's unfair, as I said before, I am ok with unfair. Because by being the rescuer, I feel like I am constantly perpetuating the cycle. I just don't want to participate in the dance of the cycle anymore.
I could handle it if there was a baseline accountability, and he slipped up, even if initially he slipped up often. I guess that's what I am waiting for - to see if he can pull it together by his own initiation. He has all the resources he needs to pull it together at his fingertips - a therapist he likes, a community that would be there for him, me. He is an adult, and it is his responsibility, and I will be there all the way if he does. So when he reached out to see the kids, I am ok with responding and setting up a visit if it's good for them to see him. But I don't want to bear the responsibility for whether or not the visit works out - if he can pull himself together and make it happen, great. If not, I just want to leave him be and see if he can figure it out.
What I am saying probably doesn't make sense in the realm of BPD, but that's where I'm at. Thanks for listening

. I am open to further suggestions and comments (and even being told that my approach doesn't make sense

)