Sorry you had to look for us, but so pleased you found us.
The good news? You and your wife can get through this. But!
She needs to be truly remorseful, she has to give you whatever details you want. (I never wanted any details of my wife's affair, but some betrayed spouses do.)
Couple's counselling might be of benefit to you, plus individual counselling, also.
You need to be checked out for STDs. Yeah, sure, of course
they only ever held hands, or she insisted on condoms, or he assured her he was clean and so on and so forth...
And one way to really show her how she has ruined your trust and faith in her, get DNA tests done on your children. This is to send her a message that she has blown up your marriage to such an extent that you can no longer trust anything she has ever said or done throughout your relationship. Well, she was able to pull the wool over your eyes during her affair, so...
A Voice Activated Recorder hidden in her car might be worth considering.
Please keep us updated on what is happening. Remember the vast majority of us here have been in your position, some in the position of your wife and some on both sides of the fence, so we know where you both are, now.