IPad – Changing Apple ID on iPad to match Apple ID on iPhone

One Apple ID can be used with multiple devices and if you are hitting a limit that too many devices are using it for a specific use (say playing purchased music on too many devices - no slots are left to authorize), you should get an error message.

The likely culprit is a network or other device specific error, but you may have to troubleshoot this:

• http://support.apple.com/kb/HT4895

Most of the authorization issues can be solved starting with the above guide and general troubleshooting might be to check that you can browse the iTunes store and ask the networking staff to make sure things aren't being blocked or take the device to another public internet to be sure it's not a problem with the network and not the device.

No, unless she is using your Apple-ID this will not be possible.
As your old iPad appears offline, this probably is not the case. You can delete your old iPad from the Find my iPhone app in order to tidy up the list, this won't disable any Apple-ID on her iPad though, should that still be on there. If you reset the device though and didn't set up the iPad with YOUR Appe-ID then you're good to go.
Also: notice that when a new device starts using your Apple ID, Apple will send you an email notifying you about that. So you can also check that even for now and in future.