Hello Audelina,
It sounds like you meant to back up your daughters phone but now you are seeing a prompt to enter her apple ID and password. From what you describe it seems as though you are running into what is called the Activation lock. Here is some additional info about that:
iCloud: Activation Lock
http://support.apple.com/kb/PH13695
And
iCloud: Find My iPhone Activation Lock in iOS 7
http://support.apple.com/kb/ht5818
Thank you for using Apple Support Communities.
All the best,
Sterling