The easiest and lower cost would be to request two cars.
Even with an eight passenger mini-Van, where would the driver be included. Same with Uber X, they can fit four, but really shouldn't have anyone up front.
I'm stating that as it was in material I had when first recruited. I'll look it back up to double check. It may be that drivers at Disney are taking families and accept that.
In larger area like NYC the passengers are splitting fares and not requesting two cars. I will follow up when I find out for sure.