Can I transfer videos from iTunes to an iPad not associated with it?
New set up will wipe out everything.

You can plug iPad into her iTunes and mark the option "Manually manage music and videos", save (sync), then plug again on your computer.

If you are careful when cross connecting, you can prevent cross-syncing the same information from two computers for this iPad, but still have each computer take care of part of the sync "situation".

other option is:
Copy the videos to her iTunes, then add them to her iPad from there.

Last option:
- Backup all the app data, videos, music and even pdf files with third party software (TouchCopy, iExplorer, PhoneToMac or any other you like). Do not backup system files.
- Set up the iPad.
- Copy everything back using the same third party software.