We are a family of 7 (with 2 children in carseats) and own a Grand Caravan. For our trip to WDW in January, we flew, but we flew out of New Orleans, which is a little over an hour away from us. We were able to fit all of our luggage for a week trip, plus a stroller and box of breakfast/snack foods in the van with no problem.
So, if you end up with a Grand Caravan after all, you should be just fine.