A few points to understand the situation abit better maybe;
1) When you were away, she chatted to other people. And unknowingly, it turned into personal conversations. It's highly unlikely that one day she just sat down and had the intention of chatting to guys. Things like this go in stages, so you call someone "brother" or "sister" first, and gradually tell them everything about life.
2) When she argues with you, she wants to run away from the issue because she hates the embarrassment. Alot of people try to hide their shame through anger, and don't want to be humiliated so they shout as a distraction.
3) You're mature, alhamdulillah. She doesn't know that many guys are evil, and they only play like innocents until they get a woman. They only enjoy the chase, but hate the responsibility. So they would harm a woman and knowing them - they're probably married and are cheating, while chatting to alot of other women too. So they wouldn't really want to marry someone who they claim they want to marry.
4) It seems that now that you know, she won't want to do this again. Many people when they go through this, only stop because of the pressure they face from others. The only reason people find excitement talking to strangers on the internet is because they feel they can give up on one if they find them boring. But marriage is long term, and that responsibility makes it feel boring.
For some Practical advice, i recommend you to block or even detail the email address, so you can't ever get access to it again [even if you tried]. That makes you stop reading the emails, it stops her from reading them, and its a step to leave the past behind you.
If you have children, take them into account when making any decision, and do the Istikharah prayer, and discuss with family seriously to those who you believe it is necessary to discuss with (without talking about it unnecessarily since that makes the bad feelings even worse.)
If you think you can forgive her, and be patient with her to move on in life. Then you can discuss that with your family, and her when making a decision.
If you choose to stick with it; Take a promise from her that she won't do it again. Something which she has to prove, and try to earn her trust. While showing signs as time progresses - if she is showing positive signs - that you are accepting it.
Try not to bring the topic back up again with her as time progresses, since that will continue to make more problems. If you can leave the problems behind, and move on - that is a good thing and mentally good for the both of you.
Try to remain thinking positive, Allah is your helper. Say alhamdulillah that it was nothing physical, and since she's said alot that it wasn't physical [while admitting the other email stuff] - it seems it wasn't physical, and many people just get the joy from chatting on the net. So this will make it easier to move on insha Allah.
Keep praying to Allah to make things easy for you, and to guide you to what is best. Then when you make a firm decision, stick to it. If you see it come up in the future, do istikharah again and discuss with family, and then make a decision. Allah will help you.
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