The PlayKids subscription is on the list of restricted content that cannot be shared through Family Sharing, because it is an in-app purchase. For more details, follow this link: https://support.apple.com/HT6389
Therefore, to be able to share a subscription, you must do the following in each of the devices with blocked access to the videos:
- Uninstall PlayKids from the device;
- Exit the Apple account, tapping: Settings, in the device's menu > iTunes Store and App Store > Apple ID:... > Sign Out;
- Log onto the Apple account that holds the subscription: insert your Apple ID and Password > tap Sign In;
- Download PlayKids again;
- Open the app and "Restore Subscription" tapping the icon with two cogwheels, on the apps start screen > scroll to Subscription > Restore Subscription;
- There! The videos should now be unblocked.
Once the app is fully unblocked, repeat steps 2 and 3 to change the Apple ID back to the one held by the person who uses the device.