I posted before that it seems to me that you may be mixing parts of marriage builders "plan A" with parts of the 180, and now it seems that you are getting advice from your DB coach that is a bit contrary to some of the prevailing wisdom on this board, particularly in regard to pursuing activities.
As you mentioned before, the heart of DB's approach is do what works. In your case, you are convinced that the warming/pursuing/physical touch/plan A type actions are working, and that is what you are being told to do by your DB coach. I mentioned before that you need to pick an approach and follow it. You should pick an approach you think is appropriate for your situation, and most importantly, that you think you can follow and accomplish.
No offense, but I dont think you can successfully pull-off all fo the 180 techniques such as detaching/GALing as espoused on this board, and frankly I dont think that approach is well suited to your specific situation. Left to your own devices, I think you are going to continue to put up with her behavior, you will not be able to signal detachment, she will know that she can keep you hooked with non-sexual crumbs. And in your case, it really seems that your wife strayed in equal parts because she allowed someone else to start meeting her needs of affirmation and physical contact, and she didnt respect you enough to fear losing you. Even your DB coach is advising you to pursue and build the physical connection. This is clearly what you want to do. So I would suggest that if you want to win her back, at least temporarily, then this should be your approach.
1) Force her to make a choice, and make the choice of coming home the easier choice. Do anything in your power to get rid of her affair partner. Confront him and make him worry. Keep it legal but make is so that your wife is a lot of trouble/inconvenience/conflict/cost to him. He should be very afraid of you.
Make the affair difficult and costly for your wife: cancel her phone and internet. Cut off all money. Cut off the car/gas. You bring home the groceries, she doesnt need anything else. She can then either leave, or file for divorce. She will need someone else to give her money to accomplish either of these. Get legal advice, know more than she knows, make her think that her affair will leave her with every other weekend, no alimony and her paying child support. Even in no-fault states, her half-time cohabitation can be used to all but eliminate alimony and can give you a lot of leverage for custody.
2) Regain her respect You have demonstrated to your wife that you are a good provider/servant, however I think she feels that she is dominant in your relationship in terms of sexual market value. Her affair partner is a loser, but you are paying for her to be with him. That makes you lower than him too. I doubt she sees you as having any sexual value whatsoever. This is the key to making her WANT to come back. You need to show high value as a dominant male, who has sexual value to women.
Make yourself be more dominant in your relationship. That doesnt mean be mean or angry, that means be calm and firm and in control in all interactions with her. Do not let her emotions affect you or sway you. Pick your reasonable boundaries (she cant leave and come back, no talking to him from your home, no gas or money for her trip etc) and enforce them without compromise or discussion.
3) build attraction Make yourself more physically attractive and let her know you have other options besides her. Without warning, start changing your appearance. New haircut. New cologne. Contact lenses. Buy a new wardrobe. Try to dress to look like you are 10 years younger, 2x as wealthy, and 2 levels more formal for all occasions.
Start working out with heavy lifting focusing on your core, arms and back to boost your testosterone and aim for a torso with the golden ratio shoulders 1.62x your waist. Squats, deadlift, bench, pullups - at high intesity intervals. Lose fat through diet (no grains, no dairy, no sugar), dont do cardio, NO JOGGING. I dont know what "vitamins" you started, but start taking DHEA and creatine to get a jumpstart, and talk to your doctor about testosterone supplements. DOnt take normal range as OK - the normal range is a huge range that half of men fall into. A youngish healthy male should be at least at the top of this range. A magical thing happens to men in your situation when they suddenly get higher levels of testosterone; most of their problems somehow disappear on their own.
Do the 180 GAL steps. Build interests outside of family that brings you in contact with other people, and women. This doesnt mean you are prowling for dates, but when she is at home expecting you to make dinner, you head out to go to the gym or drinks with friends, or a meet-up, and then say nothing about it.
3) Demonstrate your ability to fulfill her emotional needs. Your wife seems to be a physical touch/affirmation type person, so you can be there to give it to her. Go ahead and physically pursue her and give her SPECIFIC compliments/rewards. But dont put too much emotional stock into it. Do not pursue with desperation, pleading, or give her any indication of you pedestalizing her. Do not say anything to indicate you love/idolize her or that she is a good person/wife/mother. Right now she is not. Tell her something limited, try to infuse it with humor, bonus points for an occasional compliment wrapped in a slight back-handed put down.
If she rejects physical advances or the specific compliments, deflect it with humor and indifference. You are a man with testosterone and sexual energy and value, she can either accept your advances and desires or not. If she doesn't then deflect it with humor - she is missing out, or she couldn't handle it etc. Her loss. No sweat to you, you can find other things to interest you. Laugh at something on your phone, head out to the gym. And then come right back to it.
So basically, my advice is based on the fact that I dont think you are going to stop what you are doing in terms of pursuing and supporting her. So if you are going to do that, fine, but you MUST also undertake the MORE important actions of a) plan a type "sticks" of attacking the affair AND b) address her loss of sexual and personal desire and respect for you that has happened due to your lack of reaction thus far.
