Sorry to hear about his conflicting signals. I guess that it just proved the theory that reconciliation is a two step forward, one step back process.
I know exactly how you feel sitting around feeling awkward. It makes it even harder for you with your little ones: You can't just take off and go somewhere. If there is anything you have done well, that is to vent your frustration here. You did a great job not to confront him and to gracefully give him time and space he needs to reconnect himself to reality of life, with needs of his W and kids.
Healing time is very important step DURING reconciliation, but not in the process during his decision to work on M. The way I read your description, his mind is still quite clouded; those healing activities you were expecting would just freak him out. On the other hand, you are actually on a positive spin here; he is going towards your direction, granted his mind has not been fully committed yet. So keep doing things focusing on yourself and for yourself and your little ones. He still needs time to play with his football buddies.
One other thought is that you may want to have a football tailgate at your house at some point. Maybe invite H's friends over and show how much support you have for him. This could give him some reassurance that he will still have those freedom even after his coming back, if that is so important in his life. Have you done things along this line of thought? It might be a good 180 for your R.
By the way, did he ever read Smalley's book about winning wife back? It referred to many analogies about football plays. Maybe somehow you can have someone else get him a copy?
Just my few pennies worth of thoughts and not too much of comforting. Anyway, hang in there and you are actually doing fine. Let's do something fun next weekend to get us off those negative thoughts. We deserve some good time ourselves!