You want me to understand your wife doesn't get stressed, and you are the only one who needs to unwind, is that it? Or are you saying she NEVER gives you space to do your stuffs in bedroom when you need.
And why does the room have to be for only you? If she's allowed into the room whenever she wants then that is not a man cave. But if you restrict your wife and children from using the room, than that is a man cave.
And no matter how you try to justify your reason, it is wrong. You only painted your version of stress, and completely ignored that of your wife's. That says something about you.
Marriage is tiring and just like you feel the need to unwind, your wife does too. But did she get a separate room for that? No! Unless you agree she gets her own separate room, your man cave is a selfish act, period.