I'd stick to the Disney buses. If you do rent a vehcile, go with 2 cars/minivans. It will be too hard to get 10 people organized to do eveything at the same time. It's better if you do not all tour the parks together anyway, especially if you have a group of 10.
Speaking from experience, someone will always need a drink, a bathroom break, a rest, a new diaper, etc. and it won't all happen at the same time! If you tour the parks together, you will become very frustrated with how little you actually see and do. Our group was only 8 and it was very hard. When we had 11, it was unbearable and we soon split up to do the attractions.
Even if you travel to the same park, break up into smaller family groups to visit the attractions. Meet for a meal or a parade. You'll be glad you did!
Best wishes -