Jeez, LL, I'm gone for a few days and all hell breaks loose! I'm very sorry things have gotten to this point, but I'm glad that your "ultimatum" caused him to think twice about what he's doing...and that he's finally willing to go to C.
Frankly, I like what it says in "After the Affair" when couples are really trying to mend things...even when one or both might not really want to--it says to spend at least 15 hours a week alone with your S. Just spending time is what really helps. I've been trying to do this as best I can. It's kind of hard at first because you don't know what to say, but then it gets easier...especially when you're trying to meet each other's "love languages." But it takes effort, and each person has to be willing to make that effort.
IMHO, your H works too much, is away from home too much, and doesn't pay attention to the most important things in his life. If he chose to spend more time with you and the children, I think his feelings would change. I really do.