I had this same problem.
Bought a PS4 and updated my service account, and lend my old PS3 to my brother so he could play.
The service account linked to the PS4 version can no longer be used on PS3 client.
Your wife can use the client on your PS3 as long as the game is installed and her PSN account is on the same PS3. However i'm not sure how can you transfer a PSN account from one PS3 to another, but after some research i found this info: "All your PSN info is stored on Sony servers so you can access it from any PS3 by creating a new user then selecting login an existing account from the sign up. Just delete your user profile from the old PS3 then login on the new one."

Hope this helps