If H has an email account that both of you know about and he deliberately did not give you the password to it then assume that he is still using it to contact OW (or at least keeping that option open). Dagny is correct -- believe nothing he says and half of what he does. This applies even if it's what you want to hear/see/believe.
My advice would be to install a keylogger on the home computer so you can see if he is still in contact with OW. At the same time I would focus on you and make the time for self-improvement.
I like the idea of your 180 plan for the week. But don't feel the need to explain where you're going or what you're doing. He is a father, he can and should be responsible for some parenting time and you deserve some time off. If H says he can't watch the kids for an evening then say fine, get a sitter, and go out anyway.
If you love somebody, set them free. http://tinyurl.com/2empx2g