Sounds VERY stressful to me, and very crowded and I very much doubt all your luggage will fit. I think the idea of renting one car ,,even a mini van for 6 people and their luggage is not such a great idea.
Suggest you map out a reasonable itinerary and take trains. Not stressful. Tickets bought point to point well in advance can be reasonably priced.
Remember luggage has to be out of sight when parked.. so it must all fit in trunk area.
Also remember gas is expensive , roads have tolls( and it can add up) .. a car is a good idea for 4 adults to split the costs.. I do agree, but six in one vehicle sounds extremely unpleasant unless you all only bring one small 22 inch bag. Can you all do that?
PS most rental sites show clearly how much luggage will fit. Did you check.