Upwards - Your sitch sounds so similar to mine (your kids, OW, DUI). Even eight months out, I am still struggling with trying to figure out how to interact with my H. It is really hard to establish a healthy boundary with your H when you are forced to deal with him on a regular basis due to kids/finances. So I am right there with you!
Over the past few months, I have realized that my H will pursue if I back off. My H has straight up told me that he is afraid that I am moving on. Although he wants the S, he is the one the initiates emails/texts/calls. When I explained this to my IC, she used this analogy: After BD, my H put me off to the side on a shelf (like a little doll). Any time that he sees me jumping off the shelf, he gets worried, contacts me and tries to get me back up on the shelf. He does not want me all the time, but he wants to know that I am sitting on the shelf waiting for him in the event that he tries to come back.
I think that your last post is right on! You just need to focus on yourself and the kids. Let him call/text/email and just respond to kids/financial stuff. I usually limit my communications to just email/text.
There were times when I just wanted to throw in the towel and file for D. I have come to realize that filing for D will not stop the pain. I will still need to engage with my H often due to the kids. Your H is clearly in crisis (OW/Rehab). Just give him some time and space. Also, take this time to work on yourself. No matter the outcome of your M, you will come out on top! And your kiddos need a strong mommy