Hi Harrand,
Adults are allowed on all rides at Walt Disney World.
While you would be allowed to go on Splash Mountain and Big Thunder Mountain, it's unlikely that your two-year-old would be able to. You might also have issues with your five-year-old depending on how tall he or she is.
Different rides at Walt Disney World have different height requirements. For safety reasons, only guests who are tall enough to be properly restrained will be allowed to ride. The gentle rides accommodate everyone, but some of the "speedy" rides do have height requirements, ranging from 32 inches to 52 inches, depending on the ride.
To find the
information you need, go to the Walt Disney World
attraction information page. You'll see on the left, about half way down, a tab that says "Height." Click on the boxes there to see which rides will be appropriate for your smaller children.
Good luck with your planning and please let us know if you have additional questions.