I'm afraid you're just not getting it. You continue to define what's "working" as what "makes you feel good."
You also don't like that you're "not respecting her wishes," when her "wishes" are to have an extramarital affair.
Until you are more concerned with doing the right thing and fighting for your marriage than you are for what either "feels good" or "doesn't upset your wife," you have almost no chance. Yes, God Himself could intervene, and your wayward wife could suddenly have an epiphany and come to her senses, but that's rare, and you will still have to deal with the collateral damage of her additional loss of respect for you and how you handled things.