Your passcode and/or Apple ID was compromised.
You will want to change your passcode and your Apple ID password, and probably also enable purchase security.
Set a passcode on iPhone - Apple Support
If you think your Apple ID has been compromised - Apple Support
Require a password for App Store and iTunes purchases - Apple Support
Kids are really good at getting passcodes and passwords, too.
And what you were looking for; how to request a refund:
Request a refund for apps or content that you bought from Apple - Apple Support
Having watched and worked similar cases rather too often, you seemingly got off fairly lightly, too. I've met cases where the kids trashed the device settings and/or trashed the device contents. Mail account settings gone, spurious replies, swathes of files or mail or messages gone, etc.