I own a Dodge Grand Caravan, much like the ones most car rental companies use in Orlando. In February, we drove from our hometown to Syracuse, N.Y. to fly down to MCO. We had 5 adults and 2 children (ages 3 and 6) with car seats.
We were packed tight, no doubt about it, but this is what we fit in the van...
5 large suitcases, 5 good-sized cary-ons, 1 umbroller type stroller.
The stow-n-go seating systems in the Dodge mini-vans have small storage compartments below the passengers' feet in the second row. You might get some smaller stuff in those areas. Also, if there is no console between the front seats, a good-sized carry-on will fit between them, no problem.
While we were in Orlando, we hired a few different SUV's to take us around...niether of them really had as much room as the mini-van. One was a Denali (sp?) and the other was some kind of a Lincoln. Nice vehicles but kind of cramped for 7 people, let alone their luggage. Maybe there are bigger SUV's than this. I don't know.
In the van, we were definitely packed tight, but we did it for 250 miles each way, so you should be be able to do it from MCO to Disney/Port. (Tell everyone to pack light though.)
Have a good trip.