Yes, our Hs are selfish jerks. Your H is on match.com (looking for W as young as 25) and my H has an OW (with four kids, more debt than you can imagine, an alcoholic and her H is prison) because they are truly not looking for a relationship. They want freedom, so they will attach themselves to people they have no future with.
Yes, it is unfair because these men voluntarily asked us to marry them and voluntarily decided to have children. We did not force them to do it, we did not trick them. When the image they had about what being a husband and father looked like did not match reality, they bailed. They blamed us and left.
I know that you are so worried about your kids. It is gut wrenching to see what this is doing to them. But your H's relationship with the kids is his to figure out. They will be okay if you love them with everything that you have. You will have an amazing relationship with them the rest of your life. You will be their rock, you will be their home. .
I just wanted to focus on one of the good things that I see coming from your conversation with your H and to point out how your hard work has paid off. Your H has gotten to the point that he can no longer blame you for his decisions. In the wake of BD, you dug deep and started working on you. Although he did not say it, he sees it. If he didn't, I think that your conversation would have been a lot different and filled with a lot more accusations. Until he stopped blaming you, there was no chance that he would ever look inside himself. He is definitely not there yet, but it is a step.
Right now, you just need a short term plan for what to do the next couple of days. You mentioned that your H wanted three more nights with your kids this week. You also mentioned that you are sleep deprived and sick. So here is what I would propose to your H if I was in your shoes: H can take the kids tonight if he wants because you are not feeling well. H can keep the kids on Wednesday and Saturday night as previously agreed. This allows your kids to see your H after not seeing him for a week. It allows you to be able to recover from the emotional blow of last night, to hopefully get some sleep and to take care of yourself since you are sick. The rest of the days, you will have the kids. Next week starts the regular Wednesday/Saturday schedule. If he does not want tonight, then tell him you will stick with the Wednesday/Saturday schedule. It shows that you are being flexible, without giving in to his every demand.