Let me try putting something that hopefully won't get deleted.
As long as your wife is involved in an affair, emotional or physical, nothing you tell her will matter. If she wants to come to you to talk relationship, fine. But you going to her to talk, writing a letter, testing, it is all pursuing. My suggestion, either write a saying that you will not share her and until she stops any and all contact and becomes transparent with you, you are out of the marriage, or go completely dark.