Some thoughts from the other side. It was an EA that ended my marriage. I confessed it all to W, along with some old history that she knew about but never confronted me with. I shut out OW for maybe 9 months and we went to counseling and everything seemed to be getting back to normal.
In retrospect, "normal" at home was only OK as long as there was no one else interested in me. "Normal" was co-parenting and being polite and cooperating on stuff. But we really weren't all that "together."
Then OW emailed me at work, out of the blue. And I fell right off the wagon, so to speak. Because I was just going through the motions at home. I broke off contact again after only a couple of weeks, but the damage was done. Things between us of course went to he!!, and then eventually I confessed to the more recent contact. And that was the end as far as she was concerned.
Bottom line, W felt she could not trust me. That strained our relationship overall and ended what little physical relationship we had. For my part, I could see that we had problems other than the EA, and the EA was more of a symptom than a cause. At least from my perspective.
I'm not sure in your case whether it is best to pretend OW does not exist. If you are doing all you can to get H's attention and he is still (at least?) calling OW, then what is going to happen if you two have a spat?
Right now he has his cake and is eating it too. It might shake him up to know that you are not going to be his door mat anymore. Tell him you know about OW and it has to stop now or YOU want a divorce.