Sometimes people ask me for my phone to call someone if their own phone is out of battery or if they don't have it on them. Just giving my phone to someone in Kid's Corner mode would be the most useful thing in Kid's Corner for me, but it seems like I can't allow calling in Kid's Corner?
No, calling (ie. the phone app) can't be added to Kids Corner in Windows Phone 8.
When setting up Kids Corner, you can add Games, Music, Videos and App you've download from the Windows Phone Store but not many of the built-in apps as the FAQ on Kids Corner mentions...
Because they can be used to make changes to your Start screen or phone settings, Hubs and many built-in apps (such as Messaging, Calendar, and Wallet) can't be added to Kid's Corner.