Eagle, I have read your threads here and over on Newcomers. The age of 36 is not too young to have a MLC. We've had a few just a wee bit younger than that pop up over here.
So, you are the stay at home dad. What do you do when your wife returns from work? Do you stay at home or do you go out for the evening? Maybe it's time to start doing a 180 and leaving once she's at home. She needs some time to bond w/the children and what better way to do that than to sit at the dinner table and talk w/them while you are out. Nothing says you have to do this every evening...but you need to start doing some things for yourself. When you go out, just tell her that you are going out for a while. You don't need to tell her where you are going and w/whom. You could very well be taking a walk, going to a coffee shop for a cup of coffee or just sitting on a park bench, but you do need to start going out when she's home. In her mind, she doesn't think you will ever change your routine. Time to change up just a wee bit.
You do realize that the OM is nothing more than a crutch? They are using each other at the moment. He's stroking her ego and telling her what she wants to hear. While he's in the picture, he is a distraction for her. A distraction that keeps her from focusing on her issues and what she needs to do to figure things out for herself.
There is absolutely nothing you can do to snap her out of the crisis. Once it begins, she's got to go through the entire crisis and hopefully come out the other side a whole, mature person. If you attempt to snap them out of it and they come back into the relationship too soon, they will pick up where they off at a later time and it will be far worse than before. We are all fixers and this is one situation we can't fix for them. We didn't break them, therefore, we can't fix them. They have to do this on their own.
I know it's difficult living in the same house, but you'll need to start focusing more on you and your children. You will need to find some hobbies and start doing them, if you haven't already.
Please continue to ask questions, read as much as you can on depression and MLC. The main ingredient is depression. This is a long, long journey for both of you. It is not a sprint, but a marathon. Dig deeper for patience because you will need it as you travel the path.
Sit quietly, the answers will reveal themselves when you least expect them to. The past is gone, the present is a gift and you need to focus on today, allow the future to reveal itself when it is ready.