Alright, so, lets say the accelerometer will be mounted on a glove on the child's hand. There is an issue here that I see, that perhaps others on the forum may know a solution to: your child's hand will be at various angles all the time. Which since the accelerometer measures all acceleration, including that of gravity, you will constantly be getting various readings according to what angle the kid's hand is relative to the ground. For the lilypad to detect "movement", it would need to tell it (movement) apart from this acceleration due to gravity at the various (constantly changing) angles. For this reason, I don't see a way for you to accurately measure any "waving" of some sort.
Again, I urge anyone here to help out, I could very well be wrong, but my understanding of accelerometers is telling me this won't work.