Fool me once, shame on you. Fool me twice, shame on me. If you were to take her back now, it would be the third time she'd have the opportunity to lie and cheat on you. She's done it twice before, so there's no reason to believe that she wouldn't do it again. You deserve much better. You're just setting yourself up for more pain and heartache if you go back to her.
Nobody expects you to just forget about her overnight. Unfortunately, it doesn't work like that. It takes time and heartache. You have good days and bad days, but eventually you come to have more and more good days and fewer and fewer bad days. You make it to the other side and see that you can have a better life without that person than the one you had with them. You just have to hang in there and be strong until then.
“This planet has - or rather had - a problem, which was this: most of the people living on it were unhappy for pretty much of the time. Many solutions were suggested for this problem, but most of these were largely concerned with the movement of small green pieces of paper, which was odd because on the whole it wasn't the small green pieces of paper that were unhappy.” ― Douglas Adams, The Hitchhiker's Guide to the Galaxy