GC2 can be installed on multiple machines in the same household for the use of the copy's owner, but since there's no multiplayer, there's not really any excuse for using mutiple copies simultaneously as you can with Sins. Still, it's kind of a gray area so long as you both live in the same house (if not, then it is definitely disallowed).
In any case, a serial can only be regsitered to one account. So if you want to have your own set of characters on your own account, you will need your own serial.