Do I need to buy a second copy for in-house multiplayer?
According to the EULA? Yes.
According to the code. Nope 
As for why it's not working, make sure you've...
1. Updated each copy to the latest version of the game.
2. After pressing the 'Multiplayer' button, be sure to select 'Play over Lan' (or something that sounds similar) to set up a LAN game. Have your son use your local IP address (should be 10.1.1.x)
3. Enjoy!
If these don't work, please let us know
Thanks!