Let me ask you a question - do you have kids? Do you plan to have them? Because my response will vary greatly depending on the answer.
If you have kids already - I would support you trying to work this out. See if she will attend counseling with you, work out what she needs to do to provide transparency, etc.
No kids? If you never plan to have any, and you want to work on this, fine, have at it.
No kids yet, but want them? My advice is to run like hell. Seriously. You're young, only 2 years married, and she's already cheating on you? This is not someone who is a good risk for the long run. I know, because I've been there. My ex-husband cheated on me the night before our wedding (didn't find THAT out until a few years later) and had an emotional affair with her for the first year of our marriage. I left him then but he appeared remorseful so I took him back (without extensive marriage counseling - big mistake.) We made 3 beautiful children, who suffered mightlily when he had another affair when they were teens/preteens. We reconciled and did well for a few more years until he went off the rails again with a midlife crisis and we divorced. My adult children are still affected by the divorce.
So basically, what I am saying is this - once they cheat, that potential is always there in their minds. And once she has shown the lack of character and capacity for lying, the likelihood that she will revert to that when times get tough are high. If you want to take that risk for yourself, that's fine. But if you plan to have kids, think long and hard about whether this should be the mother of your child./