I empathize with you and pray to Allah to give you peace of mind and inspire you to choose a course of action that is beneficial for you in this world and the next.
There is no doubt she has committed adultery which is one of the most heinous sins in Islam. If she persists in such a relationship, then you are not allowed to remain married to her; you ought to divorce her. If, however, she is truly remorseful and has taken the necessary steps to seek repentance and cut off all relations with the man then you may give her a second chance - if only you can trust her.
For further details, I would advise you to refer to my answer linked below: