Various Things to Consider
Welcome aboard the RoadTrip America Forums!
At first blush, it seemed as though you were trying to pack an awful lot into your two weeks, but the agenda you've laid out should actually be quite doable. The one thing I would urge you to build into it though is some down time, one day every four or five where you've got nothing planned and everyone is free to do what they want, most notably get away from each other.
The other possible pitfall is with your rental van. Every rental reservation will contain the words "or similar" giving the rental company some wiggle room to substitute an equivalent vehicle (or 'better') depending on what they have in their inventory when you actually show up. But your needs are rather specific. Even if they have a Chevy Express available, you're going to want it in a particular configuration - as an eight passenger van. If it's set up as a twelve passenger van luggage space, entry/exit, and leg room will all suffer. About all you can do, however, is talk to the Miami airport rental people directly a week before you arrive, and then again a couple of days prior, so that they are clear on what you are expecting and need.
I'd also suggest that for places to stay, you look into the three major motel chain reward programs: Hilton Honors (Hilton, Doubletree, Hampton, etc.), Marriott Rewards (Marriott, Courtyard, Fairfield, etc,), and Choice Privileges (Comfort, Clarion, Quality, etc.). If you can find one program with enough lodging choices (location and amenities) to suit you all, signing up for their program should net you a free stay or two during your travels.
Finally some suggestions for things to see along your route. At the moment it seems to be a bit theme park heavy, so my proposals are going to be more education and nature oriented: Kennedy Space Center, Gulf Islands National Seashore, Weeki Wachee Springs State Park, and Big Cypress Swamp National Preserve would all fit easily into your current route and are worth checking out.
AZBuck
