Solost Well done for getting back on track and detaching from him when he came round. I'm also pleased that you are welcoming of all responses on your thread and of course you're right, Mumsnetters can be blunter and more honest than your RL friends, who have an investment in you liking them.
I wanted to progress a couple of issues with you that have been mentioned on your thread, but you haven't come back to.
What boundaries can you put in place now regarding his visits to your home and his interactions with the DCs?
It is going to be easier to detach if you are not there during his visits, or if he sees the children on neutral territory. Now, I imagine that you fear if you let him take the DCs out for the day, he will introduce them to the OW or take them there and I imagine he would be too weak to resist any pressure from OW to do that, but could he see the DCs at his parents' house?
This is probably going to bring forward telling the DCs, but I imagine they are already sceptical about what's going on and perhaps have some worries or doubts that something significant has changed in their parents' relationship.
Can you get your key back so that he cannot let himself into your home when he feels like it? As I said upthread, it might be half his house, but it is not his home.
Finally, you absolutely need to get some legal advice, because everyone else is spot-on when they say that his promises to be fair about the money will evaporate in the wind if there is any pressure from the OW and he has already shown you time and time again that he crumples whenever she puts pressure on him.
You also need to become financially independent of him, because that will make it easier to detach. That doesn't mean having to increase your hours or get a new job, it just means formally agreeing money for the DCs and some spousal support to enable you to care for them.
Getting your H to see how this will hit him financially is also yet another way to burst the affair bubble.