OK, I don't have the exact same problem, but here are a few things you could try.
1. Go to www.icloud.com and login. Select your calendar from the icons and you will then see the cogwheel in the top right corner. Click on it and enter your settings. Under ADVANCED, there is a tick box saying "Send me a copy of event invitations and updates"
2. On the shared calendar on the left hand side of the calendar you are in, it should show a list of your calendars. The shared ones are green whilst the others are just white/transparent - Click on the green one of the calendar that is being shared (The clarify, this needs to be done within your wifes icloud, not yours and she needs to click your "Home" calendar green bit). This opens up the Tick box "Email me when this calendar changes" - deselect this.
For what its worth, here is my problem. I keep getting invitations for all my girlfriends new appointments. They are coming up in the same invitations box that you get notified in when someone invites you to a lunch where you select reject, accept etc. But these just have an OK select button. I can't seem to find anything that rectifys this, and it has only happened since I upgraded to Mountain Lion, but my girlfriend has not.
There is nothing on the web to describe this problem so far and I have gone through every setting trying to rectify it. If anyone can help on this one, that'd be great.