Unless you both agreed to be exclusive then she didn't cheat on you. Now that you decided to give her another chance, did you ask her to be exclusive or are you still in the state of limbo in your relationship?
My concern wouldn't be that she went to bed with him (as I said you're not even official) it would be that she's still got unfinished baggage with this "old flame" and that is what you need to suss out. Does she still have feelings for him? Will she be seeing him keeping in touch with him? What is their history? If she's still got feelings for him then she'll not be able to have the proper one's for you.
If you decide to stay after you've got to the bottom of her "baggage" then make sure she knows you're "official" and that she's to remain monogamous with you if she wants a relationship with you.
These things have to be made clear in this day and age ... nothing can be assumed.
“The willingness to accept responsibility for one’s own life is the source from which self-respect springs.” ~Joan Didion