Sorry this all ended with a breakup whenisigonnadonow.

This revelation that you invaded her privacy was obviously a deal breaker...like you didn't trust her. Its like reading a diary without permission.
I don't agree with some posts here putting your GF down for the relationship she had with this man - they were friends who agreed to be sex partners when both weren't attached - basically a 'friends with benefits' deal. She didn't cheat on you and you were reading past conversations. Since he made it clear he had someone and neither of them cheated, I don't see the harm in them conversing as friends. Its doesn't seem like she was in any way taken advantage of and I don't think we should judge them if they were pals with benefits when they didn't have partners.
I'm sorry this didn't work out and all you can do is learn from this. I think we can all agree, we wouldn't want someone reading our private emails - its like opening someone's paper mail.