Can someone love you and cheat on you? Can they truly stop & be faithfull?

My wife cheated on me 2 times in 7 years, I just found out last month that this happened. I love her very much and want to save this marriage. We are in counseling and she has opened up to me and told me everything. She is not hiding anything from me that I know of. We have a 5 year old child that we both adore and I would hate to destroy all we have built over the years. I really want to believe that she wants this as much as I do, She seems sincere and is doing anything I ask her to do. By the way she is in her early twenty's and i am in my mid thirty's. Thanks for your Input!