Yes, we can be a hurricane in the middle of the mess.
Of what happened, I don't feel that you made a mistake going through his things with his permission. The downside it's still snooping but the upside is that you could figure the depth of the issue.
Just remember this, because I made this mistake too. Don't expect that things will be better whenever he promises you some change. People who does the cheating wants the problem to go away overnight. And that's why they fall back right in again. It takes sometime until the "drug" effect fades so they can say things that they don't really feel or compromise to things that they will repeat the next day. Because it makes them feel good and they need the next "shot".
That's why you need to DB. Learn the 48 hour rule, how to go dark, the 180, etc. The C is very important here too. Only through our behavior we are able to change their.
Mostly important, take care and focus on yourself now.