For the purchase, did your credit card get charged? Did you receive an e-mail receipt? If yes to both, on the e-mail, click Report a problem. If those things didn't happen, the purchase didn't go through.
If necessary, contact iTunes Support. Scroll to the bottom of the page in the 2nd link.
iTunes Support
iTunes Support – world wide
I recommend creating an Apple ID for each child and, as already suggested, set up Family sharing.
Apple ID – Create
Apple ID - Create or use your Apple ID without a payment method
Family Sharing and Apple ID for your child
There may be some data loss, but you can minimize it. If syncing photos with iCloud, ensure Optimization is turned off in Settings/Your Name/iCloud/Photos. Then make sure full resolution photos are on the device. When signing out of iCloud, if asked whether you want to retain data, choose yes. Messages conversations will be lost if they are addressed to the ID. See the article below for other places that the old ID should be removed. Also set up Family Sharing to keep access to your apps. Also see Winston Churchill's response in the below discussion
How to transfer all files from one iCloud account to another
Apple ID email address or password - What to do after you change
Family Sharing - Use your own Apple ID for Family Sharing
Family Sharing -What types of content can I share?
Family Sharing - If you don‘t see your family‘s shared content
Family Sharing - Ask to Buy
Family Sharing - purchases and payments
Family Sharing - Hide and unhide music, movies, TV shows, audiobooks, and books
Family Sharing – share iCloud Storage
Family Sharing - Share an iCloud storage plan with your family
Family Sharing and location
