I don't understand why you feel that you need to explain yourself to your wife or anyone else? I respect my friends who rule the roost and ridicule the ones who let their wives run rough shod all over em.
My homeboy Jody tells his wife what's up and his kids are well behaved. I don't envision them getting a divorce, ever.
My hommie Bryan let's his wife break his ass down Cool Hand Luke style. His kids are always crying when they don't get what they want. They go to relationship "therapy". I expect them to divorce as soon as their kids are out of the house, maybe sooner.
Men should act like men.
If I was you, I wouldn't budge. It's not like you're being unreasonable. Although, I'm old school, and in my book the wife comes before the kids and the parents, etc. I'm sure you'll make the best choice in what you do but I wouldn't argue. Tell it like it is and stick to your guns.
Anytimes I need male advice I consult these guys.
The Art of Manliness | Men's Interests and Lifestyle