Tony did not run the house. He cleaned it. He also nanny-ed but he had absolutely no say in any major decisions. I remember in one episode he was conned into buying something (encyclopedias? an appliance?) very expensive. Angela immediately figures out the price (because apparently, Tony can’t math) and has a fit. It is clear that Tony does not have the authority to make such a major purchase for the household. Mona has more say as she does what she wants because Angela is not HER boss.