We had a child--same age--who pulled something similar, except that it was a control issue. She lived to ruin everyone's good time. I checked out my child care options before we went. There is a day care (either La Petite or Kindercare) nearby which takes kids on an hourly basis, or there's always "Disney Day Care"--the kids' clubs--which limit you to four hours.
I did not force child to ride anything "scary"--I don't ride a few things, and we did child swap on the zippier stuff that I do ride--but if she started being a pill about a benign dark ride or being "too hot" or "too tired," I pulled out my day care threat. Also, I used being grounded from the resort pool as a consequence for un-Mickey-like behavior, and I actually used it one day.
Another possible "carrot" is to take poker chips or stickers--each one is worth a certain amount of money, say $.25--which are awarded for each ride ridden. You can award one token per ride, or have a scale based upon the intensity of the ride, and that money is the child's souvenier money.
It stinks to have to have a discipline management plan at WDW, but some kids need it, and it will end up making the trip more enjoyable for all involved.