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.
From the way you phrased your question, it appears you may want to allow select photos to appear on their devices. If this is the case, the best solution is probably to disable Photo Stream on your children's devices, but leave Shared Photo Streams on. By disabling Photo Stream on their devices, it will prevent photos you take from automatically appearing there. However, by leaving Shared Photo Streams enabled, you can create a Shared Photo Stream and any photos you place in that will appear on their devices automatically. It's effectively manual curation for what they are able to see.
To disable Photo Stream on their devices:
- Open the Settings app.
- Tap on Photos & Camera.
- Ensure "Shared Photo Streams" is set to On.
- Slide the "My Photo Stream" toggle to the left to turn it off.
If you don't want them to use Photo Stream at all, turn off both Shared Photo Streams and My Photo Stream.