If you are going anywhere alone with 3 kids, WDW is a great place to be. I have done it and am doing it again this summer for 3 nights. I do not bring my 3 to the grocery store with me. But Disney, no problem! That said, the age of riding is a real issue. My 1st 1 parent trip was with 3, 7, and 10, so I could always ride with the little. Have they been before? Would they handle missing a favorite ride okay if you can't sit together? A possible alternative... hire a sitter to go in with you. (Expensive, but possible.)
It might be cheaper if you can hire a sitter or mother's helper down there to spend the day in the park with you. I guess it would cost a park ticket plus the sitter's wages.
I googled and found one
http://vacationsitterfl.com/
From their site:
Extra Hands
Navigating parks, delegating fastpasses, and trying to keep your kids occupied in a hot theme park line is no easy task. In the midst of that pixie dust induced chaos is where our in-park professionals shine! Equipped with annual passes and knowledge of the parks, rides, height requirements, fastpass systems, restaurants and so on, having an extra set of hands and a capable guide can really save you time, energy and money!
In-Park Helpers can assist with:
-Transportation via shuttle, car, monorail, and ferry
-Bag-check points and park entry
-Navigating the parks and locating rides, bathrooms, first aid, and baby care centers.
-Advising on age appropriate rides for children based on height, age and temperament.
-Taking photos so no one in your family gets stuck behind the camera
-Mealtimes so parents can finish eating too
-Sitting off with a child if the party would like to experience a ride or show that is too intense or the child doesn't yet meet the height requirement
-Holding a spot in the line
-Pushing strollers and carrying diaper bags
-Bathroom breaks
Our in-park family helpers are right there with you to share in all of the work that goes into producing the perfect Disney vacation and aid in making it as stress free as possible for everyone involved.