Disabling Photo Stream with Shared Apple ID
If what you are trying to achieve is to give your kids' devices the ability to download apps that you purchased on your device(s), then you probably do not want to log them in to your iCloud account at all. Instead you need to go to the App Store settings, and enter your Apple ID in there, to allow the store to use your ID.

The advantage of this is that you can create each of your offspring an iCloud login of his/her very own, meaning that they can turn on iCloud backup without eating your storage, and to save their own Photo Stream, contacts, et cetera.

Also you can have them appear as different people under Find My Friends.