iPad mini 2 has encountered a problem while installing an update
Your daughter's iPad mini isn't broken, but she will lose everything not stored in iCloud (contacts, documents, likely photos will all be alright).

In order to get the iPad back to normal you'll need to restore it with iTunes on your Mac or PC (it comes with OS X on a Mac, but will need to be downloaded from http://www.apple.com/itunes/download/ if you don't already have it).

To paraphrase this Apple Support link:


Plug the iPad into your computer by using the Lightning-to-USB cable
included with it.
Open iTunes
Select the iPad in iTunes
Click "Restore" or "Restore from Backup" if you have one 
The iPad will need to be set up as if it was just taken out of the box, but it will be running iOS 9.2, the newest update.