If you have insulation, a tight envelope (skin, exterior), and central air conditioning, in Florida, you TOTALLY NEED A VAPOR BARRIER.
If you do not have a vapor barrier, and you are cooling and dehumidifying the interior of your house in the summertime, you're sucking heat and humidity through your walls. Vapor barriers will stop the humidity, like insulation stops the heat. Once the humidity reaches a cool surface (backside of drywall?) it will condense. Condensation will lead to mold, rot, or both. A vapor barrier on the WARM SIDE of the wall assembly will prevent the moisture from condensing in a place you don't want it.
The problem will be repairing or applying a vapor barrier to a wall that already exists.
From the outside, the layers of a typical brick veneer wall assembly are: Brick, VOID (MUST REMAIN CLEAR, usually 1" - 2" airspace, should be free of mortar slop), vapor barrier, plywood sheathing, studs/insulation, drywall.
In this condition, the humidity will move through the porous brick, condense on the vapor barrier in the void, and roll down the wall. At the bottom of the wall, flashing will direct the condensed water to the weepholes in the brick (you have weepholes, right?), where it will dribble back outside. Provided you've not got a lot of mortar slop in the void, which prevents the water moving back outside and keeps it trapped in the wall.
If your contractor isn't willing to have a reasonable discussion with you, or to effect change orders to your satisfaction (upgrading door handles, plumbing fixtures, etc), you need to fire him. I've been in the industry for years, and the first time I hired a contractor I did it all wrong. It's easy to screw up. I'm still fighting with my plumber, who has told me I'm a bitchy pain in the *** and have "no business snooping around in the plumbing codes".
Things to google: "Rain Screen" "Vapor Drive" "Brick Veneer Wall Assembly" "Hot Humid Climate"