How can I restore my child's AppleID?

Contact Apple as outlined in this document https://support.apple.com/HT208856

Since you have not provided any information indicating why the Apple ID has been disabled, it has been indicated by Apple in this topic https://discussions.apple.com/thread/253232167 and this topic https://discussions.apple.com/thread/253225002 that it is not considered helpful for us to provide a list of scenario-specific solutions. Ignore the fact that this recommended solution appears to only apply to one specific situation, you apparently now must contact Apple and ask them to help you if you post and simply state you have a disabled Apple ID. They alone may refer you to the solution you need.