It is crucial that you and your wife are going through the pain (of both) openly.
Two factors:
People develop and deepen their connection through adversity. The mere fact that you are both suffering through this, her for the pain she sees she caused and you for being betrayed, bonds you.
Second and probably most important:
Talking openly about the betrayal, even its most sordid aspects while excruciating for the Bs and in a minor part for the WS,has a killing blow effect on the affair.
Because it breaks the intimacy between your wife and the other man. It was their thing, their intimate time, you were cast out.
Revelation rips its furs out. Kills that intimacy as the betrayal killed yours when it happened.
Yes it is disgusting, yes it is repulsive, yes it is a torture for you and shameful for her.
But exposed shit stops smelling, begin decomposing, it dies.
The moment the wayward comes completely clean, there is no more "our thing" is no longer intimate or cute in any way. Is naked, in the open light, where you both can see it’s twisted deformity and the disgust that you feel will be felt by her and likely shared since she is healing.
It doesn’t resurrect your relationship that was before, that is dead. But it kill the cheating relationship that murdered it. And that also dies, fantasy and imaginary romance replaced by a brutal truth.
It was he lowest meddling in a can of worms.
If you ever done something you aren’t proud of, this is a magnitude greater.
Once both relationships and their intimacy are dead, you are even. Not exactly a blank slate, but you leveled the Plainfield. Not just the ruins of your story, but now the ruins of the affair lie next to it.
Probably there something new can be rebuilt.
A new intimacy that may spawn something else along the way.
You are not verbalizing this, but your emotions told me this story.