What kind of lighing are you using? Continuous, I'm presuming.
With today's cameras, you're better off raising the ISO to as much as 800 to get a higher shutter speed. Not even 1/250 is really that fast for critical sharpness. You can remove noise by various methods, but you can't remove motion blur.
As for hyper-active kids, do this:
Get yourself an inexpensive radio remote shutter release. Put the camera on a tripod, focus it on a spot with a moderately long lens, put the kid on the spot and then get out behind the camera and as close to the kid as possible, just out of the camera's field of view.
This is why: Small children depend on seeing your face and expressions for a large proportion of communication. When you're standing two or three meters away with your face behind a camera, you've lost most of your ability to communicate with them. By getting your face from behind the camera and moving closer to them, you will communicate better and be able to "rivet" them more effectively to one spot.
I didn't realize how well this worked until I watched a friend of mine who specializes in commercial photography of children.