You know, Soccerdad, you can't keep a marriage going on good intentions of not putting your children into a divorce.
Changing habits is a long process, could it be that you both stopped counseling too early or that just maybe you have to go back to it? I'd say it's the most reasonable thing to do now.
Your commitment to your marriage is admirable and I guess you owe it to your daughters to remain in it or step away from it with a clear conscience that you have done all that's possible and have no regrets whatsoever.

I know this is going to sound a bit harsh, but putting another person in between gives you the wrong idea that the other relationship is all love and tenderness, but that relationship does not have to face all everyday problems (including a teenage girl) that your marriage is facing.
Besides, feeling treated not too well by your wife and knowing that this other woman had always loved you and is somehow waiting for you, of course melts your heart out but your true feelings are also confused by this expectation and this feeling that you somehow wronged her before and you can do it right now.

I think the second woman needs to be put on hold now and I agree that if you ever step out of your marriage it would be better to live alone first, and do not step out of it because of another person.

I would go back to what your wife says that you don't understand her. Well, I guess that if i was rising 3 kids, with all the problems connected and my husband would speak a different language, not really understanding what I am going thru, I admit it could drive me nuts.
Could it be that she is yelling out of desperation of seeing that your mutual feelings are not what they used to be and that her life is very trying?

Even if your marriage comes to an end you need to have a good relationship with your wife for the children's sake so you need to find ways to have a good communication with your wife, whatever comes out of it.

If food is the most reassuring, safe and best thing in you'sr wife life now, would you still judge her for her weight?