Interactive children's game - wireless networking and motion tracking

Firstly, I'm very (very) new to arduino, so please forgive any errors relating to terminology or technical details.

I'm an industrial design student, looking to integrate some interactive features into an upcoming product. I've wanted to start learning arduino for a while now and this seemed like the perfect opportunity. Conceptually I'm wanting to design a toy/game that gets kids to be more active. Here's what I need help with:

I want the kids to carry around an object, for example a "ball", that keeps track of their movement. This is not to say that the exact path they follow must be recorded, for all intents and purposes they can run around in a circle if they want, as long as they're moving. Instead i want to be able to convert their movement, ie the changing location of the ball, into "points", thus incentivising them to be active. I was hoping anyone had any suggestions for me? So far I've considered using a pedometer, inertial trackers, GPS etc.

Next, I need a way for the "ball" to communicate wirelessly with the other devices in the system. I want each child to wear a "watch" with an embedded RFID tag that is read by the "ball" (which will obviously require an RFID reader module) so that the system can assign the relative points to the user, or team, that is carrying it. The system (console) will randomly select who should be in possession of the ball and alert that user, via vibration/LEDs etc in their "watch", that it is his/her turn to carry the "ball". If they do not use the ball to scan their watch in a predetermined amount of time, they are penalised and the system will select a new user to carry the ball.

Finally, I need the "ball" to communicate with a main "console". When the balls are returned to the console, the points are essentially "transferred" to the console. The console determines a winner, based on the highest number of movement points "collected", and then displays who the winner is to the users.

In a nutshell, I need to know the best way to get the devices to communicate with one another, in addition to finding the best way to track the movement of the ball and somehow convert the work done (to move the ball) into "points". Any help / input will be greatly appreciated. Thanks in advance.