As long as the OM is in the picture, your M will not recover. The affair is going to have to die a natural death at this point. Your job right no is to leave her with a good picture of you, one that she could return to when her A ends- and it eventually will. You are the father of her children and the natural best choice to be her husband. Of course, she can't see that right now. She's in the fog and this OM is who she considers to be her "soulmate" right now.
The two people in any affair of this sort are very selfish. They may say they care about the other person, but what they REALLY care about is how that other person makes THEM feel. It's selfish. Eventually, the other person will start to have conflicts with your W, and since they are both selfish, and are looking for perfection from the other person, it will begin to unravel. Most affairs blow up in a couple of months to a couple of years (sooner if they are closer together and have more time to disappoint each other). When that happens, your W has to have good last memories of you. Many folks make the mistake of shutting the door on the WAW by being disrespectful and hurtful and may never get their spouse back (if they even want them).
I suspect that this OM won't be able to meet all of her needs, as you can now that you are improving your relationship skills. For certain, he cannot provide her with a complete home as the father of her children. You have the advantage here whether you realize it or not. Sit back, be the bigger person, and wait for the OM to blow this up for you.
BTW, what do you know about this guy? Is he married?