He has to decide who he wants to hurt now.
I'm going to go ahead and second this, and expand a little bit.
Since your H seems to think he is some kind of knight in shining armor, and hero man, why not explain to him in a way that he can understand...that the knight in shining armor saves the princess. He doesn't rescue EVERY princess- just his. Cinderella's prince didn't find her shoe and then run out during their wedding and say, "Hang on, The Little Mermaid needs saving too." Snow White's prince doesn't kiss her awake, and then insist on stopping at Sleeping Beauty's palace to kiss her awake and save her too. They left that whole other kingdom sleeping, because Snow White's Prince was HERS. She didn't need to share with Sleeping Beauty. Cinderella didn't need to share either. The whole point if a KISA is that he's YOUR KISA. That you don't have to share. That he rescues YOU and is hero for YOU, not some other chick.
By trying to be KISA to two women, he ended up being KISA to ZERO women. There is not a way that he can come out of this looking like a hero. He needs to decide if his wife and children are more important to him, or if this OW is more important, but he can't have both. He already hurt her, he already hurt you. By leaving things in limbo, he is just twisting the knife in your back. You can't ride two horses with one @$$, you know what I mean?I have been cheated on by 3 different men, and I have more DDays than anyone ever should. I am here, just trying to pickup the pieces.
At least the current man "only" cyber-cheated.
"Love means never having to say you're sorry."