Since she broke up with you first and then slept with her 'friend', technically she didn't cheat on you. Tho I think it was disrespectful to your long relationship and rather fast work. I'm guessing she had a thing for this guy well before your break.
So I'm not sure what you distrust about what happened, unless you think she was seeing him before you broke up.
But the fact she wants to keep contact w/him after what happened is wrong. Its almost like she wants to string you both along. No girls is worth this hassle. If you really want to give it another go, tell her she needs to cut contact with this guy if she wants to be with you. Meantime, YOU should work on trying to meet her emotional needs so she isn't looking to get them filled outside of your relationship. You both have to give something to improve.
I'd give this a few months, under those conditions. If things don't improve then you should each try to find someone more compatible.
Second thoughts can generally be amended with judicious action; injudicious actions can seldom be recovered with second thoughts.
--Cyteen by C.J.Cherryh