Hi, Arianna! This is a tough question, since I don't know much about your family - except that there is always someone else to play with in a family this size! I think your best bet is going to be to make a list of the must do attractions at the other theme parks, and seeing which is the shortest list.
If it were my family, I think our short day would be Animal Kingdom. I'd plan to get there as early as I could (using Extra Magic Hours if you are a resort guest and it's an option), and do the most important rides first. Kilimanjaro Safari is a must do for all of us, and if the weather is warm enough, Kali River Rapids is another must see attraction. After that, Festival of the Lion King is our only other not to miss attraction. The rest of the park is awesome, and we love spending a whole day here admiring the animals and checking out the other attractions, but our must do list is the shortest here.
Have the kids check out
www.disneyworld.com and look at the planning section for each theme park. Come up with a list of the things you can't miss, and determine based on the shortest list which park you think you could do in the least amount of time.
Have an incredible vacation!