Both are impossible. Can't put the PC in the living room because of the small kids, can't use the TV in my office because previously documented evidence of my office being destroyed by her.
Well here is your answer. Basically, make cleaning the god damn office (and locking it from everyone else in the home) mandatory before you budge an inch. I know you love your wife, but she is by your own words a stay at home princess wife who lets the house go to hell. She has no leg to stand on to bitch at what you do with your personal time, if you are loyal and meeting all your other commitments. Continue reclaiming your balls, man.