Simply put, you've got ten solid days of driving ahead of you to make this trip comfortably, and more importantly: safely. Add in the eight days that you plan to spend in your three destinations and you literally have NO time left for ANY sight-seeing. The driving time estimates you get from computer-based mapping routines are pure fantasy. They do not allow for any stops: no meals, no fuel, no bathroom breaks, no traffic congestion, no nothing. They assume you'll be driving at or above the speed limit every second of every minute of every hour. Not going to happen. Period. With five people you'll be extremely lucky to cover 550 miles or so on any given day if you stick strictly to the (boring) Interstates. 700 miles on the best day you could imagine is simply out of the question. You either need to add significantly more time to this trip, cut out NYC/DC or Florida completely, prepare for a lot of "Are we there yet?" moans from the back seat, or some combination of all three.
AZBuck