Hello Trust29,
Are you showing that your iCloud contacts are enabled on both your device and the child's device? If needed, the article here can help: Set up iCloud for Contacts on all your devices
If you're seeing contacts are turned on, be sure you can view your personal information and your child's contact details. You may need to restart both devices to test. However, if you can view the information as expected and the previous steps for renaming the devices to check hasn't help, reach out to Apple Support directly to further assist.
Contact - Official Apple Support
Contact Apple for support and service - Apple Support
Best.