Hi there Bill and welcome
For this to happen you need to register the Kindle App with your wifes account, not yours as the library belongs to your wifes account.
To do this
From the Kindle reading app Home screen, tap the Settings icon.Under Registration, tap Update, and then tap Deregister this Kindle.
Then register it with your wifes account and the library will then be available.
If you have any problems, or would like any additional information or assistance, please do not hesitate to let me know.
Else if you can take a second to rate my service by clicking one of the stars at the top of the screen then submit, that would be greatly appreciated.