I guess the problem he is having is with the settings he uses. I am sorry if I am wrong, but *most* people would get in very close with 18mm, at say f/5.6 1/60 (this is what the auto mode may give). The subject would be running around, and impossible to track from that distance, and the shutter way too slow. The on camera flash on ruins the picture completely.
How about this for a start for indoors: get your 70-200mm, and set the camera to M. Select ISO 200-400, 1/250s and f/4, AI-servo, and put the 430EX on (+2/3 EV setting, 50mm zoom) pointing to the ceiling. Then it is foolproof from there.
For outdoors just set it to Av, f/4 and AI-servo for action. Forget the other lenses if you are shooting your kids.
I also strongly recommend reflectors (less than a tenner on ebay) and they make an incredible difference.