i assume your wife is a teacher or a doctor?
the "housewife" visa your'e talking about only grants you residency, it does not permit work. you would have to apply for a work permit through a registered company in order to get a labour card.
techincally the issues are NOT related, so yes you could find employment under your wifes sponsorship, else your employer could arrange residency for you in your own right (off of your wifes sponsorship).
the same is applicable if the roles are reversed