To fix this you need to migrate you daughter to her own, separate iCloud account with a separate ID. You can continue to share the same ID for purchasing from the iTunes & App stores; it does not need to be the same as the ID used for iCloud.
To do this, on your daughter's phone, if she has any photos in photo stream that are not in her camera roll that she wants to keep on her phone, save these to her camera roll by opening the my photo stream album, tapping Edit, tap all the photos, tap Share and tap Save to Camera Roll.
Once this is done, go to Settings>iCloud, scroll to the bottom and tap Delete Account. (This will only delete the account from her phone, not from iCloud. Your phone will not be effected by this.) When prompted about what to do with the iCloud data, choose Keep On My iPhone. Next, sign back in with a different Apple ID to create her new accoung (if she doesn't have one, tap Get a Free Apple ID at the bottom). Then turn iCloud data syncing for contacts, etc. back to On, and when prompted about merging with iCloud, choose Merge. This will upload the data to her new account.
After her phone is on a separate iCloud account, to un-merge data such as contacts go to icloud.com on your computer and sign into each iCloud account separately and manually delete the data you don't want from each account.