Nope, that clause isn't in our lease or the early 1980s-template used by many co-ops. If it's in your lease, however, then it sounds like you're covered and the board could not overturn it without a supermajority vote by shareholders.

You should ask a lawyer to confirm the zoning laws in your case. For example, the NYC Zoning Resolution states that a home occupation "occupies not more than 25 percent of the total floor area of such dwelling unit or rooming unit and in no event more than 500 square feet of floor area." Furthermore, you're only allowed one employee who doesn't live in the apartment. If you meet those criteria and the related ones specified in the zoning laws, and your lease contains the clause you quoted, then you should be okay, regardless of any house rule to the contrary. (I'm not a lawyer and you should definitely consult one if you plan to ignore a house rule because you believe it is unenforceable.)