Hi Lil718allison,
We'd love to answer your question for you. The reason. you may not be able to share a photo album with the child's device is likely because Apple Watch isn't compatible with the feature. You can check out the information we've provided below to see compatible devices and software versions.
"iCloud Shared Photo Library is only available on an iPhone with iOS 16.1 or later, an iPad with iPadOS 16.1 or later, a Mac with macOS Ventura 13 or later, an Apple TV with tvOS 16 or later, or a PC with iCloud for Windows 14 or later. If you open the Photos app on a device that hasn't been updated to a supported version, you won't see the photos that you moved from your Personal Library to your Shared Library. Learn more about iCloud Shared Photo Library.
To see your photos, use a device updated to a supported version of iOS, iPadOS, macOS, tvOS, or from any device with any software version on iCloud.com."
Reference: If you are missing photos after joining an iCloud Shared Photo Library
We hope that helps.
Cheers!