You may not like my answer, but only the expensive digital cameras can do true hi-speed shots. It is getting better and cheaper every year, but your babies are getting older too, so it is a question of how long you are willing to wait. I had a budget camera, I used A LOT, and actually learned to anticipate my DCs upcoming reaction, and press the shutter a half to one second BEFORE he was going to smile, stick out his tongue... whatever. I now have a Nikon D50, which isn't cheap, but I don't have to anticipate what will happen anymore.
A tip though: you can cheat with speed by changing the shutter speed. Default is 200 or 400. If you get a camera that can use 800 or 1600, then it needs less light to take the same picture, so a faster shutter speed. (Actually it is all digital so it is just taking in less pixel data to emulate how traditional film works at 800 or 1600 but now it is theoretical rambling.) Also, nothing is free - setting to 800 will result in somewhat more grainyness (depends on how picky you are) and 1600 will be A LOT of grainyness.