Sorry you got a little off track and got hurt in the process. Do you know who he was texting/talking to? If not, or even if you do and it hurts you, try your best to focus on the good things right now...improved communication with H, him asking to join the family at the movies, etc. You really need to celebrate the baby steps (and they are great ones!) and not get mired down by what you found.
When my h came back to me, it was over a process of events happening...like the things that are happening for you and your h! I was pretty well detached once he started coming around again, and I looked at the situation with NO expectations and with the attitude of, "if the worst thing that happens is we get a divorce but can have a good co-parenting relationship, then that's pretty darn good!". I think he saw that in me, with total lack of pursuing, and that was very attractive to him.
I'm not saying this will happen for you as well, but I do see a lot of similarities in our sitches and see your h is still quite attached. So...take a deep breath, enjoy the time together as a family and keep working on that attitude of detachment.
Also, if you feel like you'll be tempted to snoop again, maybe you should separate accounts. We did when we first separated, and that was a huge relief for me.
