oompa, people who cheat do not respect themselves. It has little to do with your wife, your marriage or how much your wife puts out or nags about "reaching out." A therapist who tells you to cheat is an idiot. If you respected yourself, if you thought you deserved to have a good life and a spouse who loved you more than her church memes, there would be no question of cheating, only the question of how do you change OR leave your present situation. If you don't respect yourself enough to be with a woman who treats you with respect, how on earth do you think you'll be able to pick a mistress who respects you?
If you don't respect yourself, at least behave as though you respect yourself. Do the right thing, either respect your family and your promises, or tell her you are through, and get out. Don't two-time your own promises.