I could be off base. It certainly feels like I'm letting her win. I suppose it doesn't have anything to do with masculinity in the grand scheme of things.
You might be right, in some cases. However, I don't think it's healthy for you to look at who is winning. When someone is showing the type of behavior you see in your W, and when kids are in the middle of it......you protect your child. It is a toxic environment, and it appears to be getting worse. Frankly, I don't see her changing while you stay there. Staying there and battling it out is not winning, and it's not fair to the boys.
In this particular case, I don't see masculinity having anything to do with it. Don't look at it as if she's kicking you out. It is your choice to leave.
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!