Legal Question in Construction Law in New York

Re: Do I have to sue, or can I file a claim?

"Additional insured" means that if someone had been injured, or property damage inflicted during the performance of the work, the contractor's insurance company would defend and pay damages awarded in _that_ lawsuit. While it is possible (though not very likely) that the contractor's insurance company will defend your lawsuit over the shoddy work, you do not have the option of simply filing an insurance claim.

The usual way to go with these problems is not to pay for the work. Didn't your coop require you to have an architect? Didn't someone inspect the work (e.g., your architect)? Before you file the lawsuit against the contractor, do not overlook the viability of a malpractice lawsuit against the architect, either instead of or in addition to the lawsuit against the contractor.