iTunes – Using Apple TV Without Another Device for iTunes Store Account

The authorization link is between the computer and the Apple ID, not any particular iTunes Library. So, no, you don't need the library to break that connection. You can create an empty library temporarily, just to get iTunes to launch, then use Deauthorize This Computer.

If you throw that computer in the garbage, you can always go to your iTunes account on another computer and click "Deauthorize All" to remove all authorizations at once. You can then reauthorize your current computers as needed.

Yes. That setup is preventing all of your devices from syncing.

iOS devices allow you some flexibility regarding what Apple IDs you use with what services. For example, you can have a different Apple ID for iMessaging, and a different one for iTunes purchases, and yet another one for iCloud. The problem comes from iCloud as anything that is related to iCloud can only sync across 1 Apple ID. It just so happens that Photostream, and Safari bookmarks are two iCloud services.

The problem is that Contacts and Calendars (less so) are often synced through iCloud, as well as Reminders and Notes. Also, her having another iCloud account means she gets 5GB free storage and you two don't have to share that.

So, you will have to decide what functionality you want to give up to gain different functionality. If Photostream is important to have consistent across all devices (or Safari bookmarks), then you will have to do what you thought - delete her iCloud account and add yours. Note, you don't have to delete her account any more then select "Delete account" on her iPhone and iPad. Generally speaking, this just signs out of the account.

Unfortunately, like you thought, there is not a way to have two iCloud accounts signed into on one devices.

_{Personally, I wish Apple would develop a "Shared" Apple ID system which would allow one to share certain services such as Photostream, yet keep Mail, Contacts, and Reminders separate.}