I'm not sure that Amazon cater for multiple copies of the app on a single device but I may be wrong. What happens when you log into Amazon on each copy of the app?
If multiple logins on the same device is supported it will "just work", but I suspect it won't. If this is the case you may be out of luck, although a work-around would be to create a third "Kindle user" account on your Nexus 7 to be used by both you and your wife and install a single copy of the app to that account.
