What is your H doing to help his love grow? If he is not a very active participant, putting in effort to bring back the romance and loving feelings, then I'm not sure that he will ever feel satisfied and that what you have is enough. And neither will you. He cheated on you. The onus is on him. Obviously you have to work together but you are coming from such a deficit that he needs to be doing more of the heavy lifting now.
What is he searching for? The thrill of an illicit A or a mature honest loving partnership? Is he holding onto pre-A resentments? There is a lot of emotional work to do--is your H up for that? Based on your post, it doesn't seem like it.
It sounds like you've been putting in most of the work. You know you can't continue that. He has had you in limbo for many months, which is just so unfair to you.
I think at some point you need to come to a decision to start the 180 for yourself. I can imagine how scary the prospect of being on your own with you children is, but at the same time there is so much possibility for you: self-respect, knowing that you are worth so much more, and showing your children that you are worthy.