Quick question: Is there any particular reason you're flying down to FL for the cruise? Have you checked out the great cruises leaving out of ports in the NE? Carnival also cruises out of the Port of NYC. Granted the cruises are longer (8 nights Eastern Caribbean), but you may find the cost difference offsets the flight costs. That's the case for my family... we can take an 8 or 9 night cruise out of NYC or NJ for about the same cost as flying to FL and taking a shorter cruise. It's waaaaay easy to park at the port (though it isn't free, the cost is pretty reasonable for what you're getting). Let's see drive to port, get on ship, be on vacation or drive to airport, get on airplane, get to cruiseship, get on cruiseship, be on vacation? Trust me, driving to the port is MUCH easier.
Regarding cruising in August: Not a bad time to cruise. Pack enough dramamine for everyone. If anyone is prone to motion sickness, they should at least take one in the morning and at bedtime of AT SEA days to ward off symptoms (doesn't work after you've already gotten sick). If anyone does get really motion sick, the doctor on board can dispense medication that will help get rid of symptoms and prices are usually reasonable (had to take DD and get her a suppository med. when she was 3 and got really motion sick... now we give her children's dramamine when I take mine).
Traveling with 4 in a cabin isn't that bad. We do it, though my kids are young yet. You're really only in the cabin to sleep and change clothes so space really isn't a huge issue. Pack a nightlight so the kids can see enough that they don't step on Mom or Dad if they get out of bed at night to use the restroom.
Especially since you're travelling with your kids and during hurricane season, get
travel insurance. I get mine through
http://www.insuremytrip.com. Get a policy with health coverage and medical evacuation (it costs tens of thousands to be medivacced of the ship, if necessary). I think a policy costs about $125 for my family of 4. Well worth the piece of mind.
I've never cruised on Carnival, but we have cruised Norwegian (out of NY) and it was decent. My family truly loves
Royal Caribbean's Explorer of the Seas out of Cape Liberty, NJ, though.... ice rink, mini-golf, rock climbing, arcade, parades through the mall... LOTS of family stuff to do.
Good Luck!