Many games like this throughout the years have prohibited multiple people in a household from playing together. Simply because you could multi account and pretend to be 2 or more people. All your reasons for why it is silly you and your wife can't play together are valid, but you have to just refer to the #1 reason.

Some games back in the day you couldn't even play unless you had a mail account through your ISP that wasn't free. This kept people from using yahoo or hotmail accounts and getting 2 accounts on some of these browser games. It was also used in some games to prevent spies, and to tell you the truth it seemed to work pretty well. I remember 1 star wars game that looked really cool that I actually never got to play because I had no ISP email.

So it sucks you have some boundaries but keeping a game with integrity has to come first.