Mama
I was struck by goal number 1 and your awareness of the last time they talked. I wonder if a good goal for YOU (not H and not R) would be to stop snooping completely on H's contact with OW. I know how difficult this is. Even when I have sworn it off, some random piece of info will hit me over the head because H is sloppy (consciously or subconsiously leaving a trail I think.) But, as far as you can control it, think about a moratorium. You will know when he is done with her, because he will change with you - in particular, goal #2 will come to fruition.

Also, I wanted to point out how great it is that you are enjoying your day at the park with the kids. This is how us Moms GAL, I think. I'm glad you are seeing some ways to do that without leaving your kids and getting a job. Kudos.

Now, as always, I have to offer the disclaimer that I my marriage is in a probably death spiral, so take my advice with a grain of salt...but take the compliments at face value. I think you are doing great.
erin