There are several ways to approach the curation/kid-friendly problem. You can have simple curation apps (which are banned in the current appstore AFAIK) that are not full stores but simply point to an app store (apple or non-apple). You can have websites that link to apps that have been vetted. On the iOS side, there could be a specific kid-mode that prevents certain APIs to be used. I'm thinking no video, audio, location/tracking services, no ads (unless the ad-network takes responsibility), etc.
Apple won't brand any particular app-store as kid-friendly, or otherwise endorse them.