Would be easier to log out of your wife's account (at the bottom of the featured tab) and then sign in as you - you can then restore your purchase on her iPad. That's what I do - you can then just sign your wife in again and all apps will work. You will just have to re-sign in again if there any any updates to the sling player app.
Thanks for using our Answers Forum. I understand that you had a question about the Slingplayer for IPad app.
You are allowed to download the app onto 5 different IPads for the one purchase of $29.99, you would just have to access the same Itunes account that you purchased the app through. As you said, only one person is allowed to access the Slingbox at a time.
Hope this helps.
Sling Moderation Team