One thing I think you'll have a problem with is extra drivers on the rental agreement. Unless one person is going to be the only driver for each van, you could run into a problem. And I'll tell you flat out, if it the rental were going on my name and credit card, there's no way I'd let anyone else drive. Your two or three drivers will be very unhappy playing chauffer to everyone the whole time.
I like PP's idea of each family being responsible to rent their own car. If two small families want to go in together, that's up to them. But in reality, it will cost less to rent eight compact or mid-size cars that will comfortably accomodate a family and luggage than two 15 passenger vans--which generally run around $850/week (plus milage!) and still won't hold all the luggage, or even five minivans which would probably be about what you need. Another thing is that if some "families" are only a parent and one child, while others are two parents and three kids, if you are splitting the cost of the van rentals on a per family basis, smaller families are subsidizing the larger ones, which IMHO leads to a lot of resentment.
If you have an Entertainment book, check out some of the deals in there. I just saved about $80 off rack rate for a four day rental in California next month with an Entertainment rate and code!