Your device probably doesn't meet the requirements.
Which iPad Mini do you have and what version of iOS is it running? Get this info, which you can find in the Settings/General/About and next compare it with the minimum requirements to run the Minecraft PE app on the app store or for more detail here: Minecraft Gamepedia PE System Requirements
If your device doesn't meet the requirements, then don't be surprised if it doesn't work.
Here is a solution to backup your Minecraft PE files and put them back on your iPad once you've uninstalled and reinstalled the app:
Step 1 : Press the "Recents" button on your device and swipe Minecraft to close it. This will completely close the game and stop it from running in the background.
Step 2 : Download a File Manager app on your device, or connect it to computer. This will allow you to access the file system of your Android device. There are several free file explorers available on the Play Store. ES File Explorer is one of the most popular. If you connect your device via computer, you can navigate through the folders just like you would with Windows folders.
Step 3 : Start the File Manager app on your device. You will see a list of folders on your device. You may have to open the "sdcard" folder to see all of your system folders, depending on your device. You don't need a file manager app if you connect your device to the computer.
Step 4 : Open the games → .com.mojang → minecraftWorlds folder. If you are using your computer, connect your device and select it from the Computer window (Windows) or your desktop (OS X). This will display a list of folders labeled with all of your created worlds, both Creative and Survival.
Step 5 : Open the folder for the Creative world you want to transfer. You should see a "level.dat" file.
Step 6 : Copy the "level.dat" file. Android - Press and hold the "level.dat" file and select "Copy" from the menu that appears. Computer - Right-click on it and select "Copy".
Step 7 : After the backup you go to the same folder and paste your copied files there. If your daughter(s) boots up minecraft again she should have her worlds again.
NOTE : This only saves the world, the player data might not be saved.
Best Answer
Okay, so this is a multi-point answer, well, one thing at a time.
First of all, you want to know if you can copy worlds via a computer. This is doable, even if the iDevice is registered to another PC. Being registered to another PC means you cannot perform an iTunes Sync of the data, but basic iTunes file transfer capability is available (unless, since you say it's a school iPad, they locked it, but that's another affair, and it doesn't have anything to do with the PC you are using). Since you did not specify which OS you are using, I'm gonna provide an answer for the three most used:
Windows/macOS:
documents/games/com.mojang/minecraftWorlds.Ubuntu:
documents/games/com.mojang/minecraftWorlds.And now about copying worlds via iCloud; the answer is: no, you cannot. Simple as that. Even if you run an iCloud backup, it still won't sync your worlds. It's actually not a very good idea to use iCloud as a backup solution anyway.