One other bit of advice for the OP ... if your child is NOT tall enough and you decide to try and skate through anyway, please do NOT cause a scene when the CM says "I'm sorry, but no."
It is not the CM's fault that your child is too short or that the height requirements are set as they are. If you feel it necessary to contest the measurement, feel free to ask for a manager, but understand that the manager is going to measure your child too. So if you go in KNOWING that your child is too short, the manager will discover that too.
If you have issue with the height requirements themselves, feel free to stop by Guest Relations and register your complaint.
But please remember that the CM is simply doing their job. They get no delight out of denying your child a spin on Space Mountain, and they're not doing it as a personal vendetta against you or your family. Yelling at them will not get your child on the ride. Bribing them will not get your child on the ride. Making a scene will not get your child on the ride.
Also ... if there is a ride that your child wants to ride but cannot go on because they're not tall enough, be sure to ask the CM for a "When You're Tall Enough" FP. Most of the rides will give your child a fastpass to use when they ARE tall enough, that will take them to the front of the line.