As kat indicates, not a trivial project by any means. However, starting with the most
difficult part kind of goes against the idea of the learning curve, especially for someone
not well versed in electronics. I would start by learning to program the Arduino first.
For motion tracking, I would try a 2-axis or 3-axis accelerometer. Can be had for $30
or so, and would be fairly easy to imterface to the Arduino. You don;t need to track
the exact path of the kids, just get a good feel for their motion.