Hello lrp1970,
Thank you for the details of the issue you are experiencing with having a shared Apple ID. I can definitely understand the desire to keep your information separate, and there are a few things you would need to look at.
The music purchased from iTunes cannot be transferred to another Apple ID, but it is important to note that you can use one Apple ID for the iTunes and App Stores and a separate Apple ID when logging into iCloud, FaceTime, and Messages. You may want to continue sharing the Apple ID for the iTunes and App Stores, but I definitely recommend having a separate Apple ID for iCloud, Messages, and FaceTime.
I recommend reviewing the following articles for more information about creating and using an Apple ID:
iTunes: How to set up an Apple ID within iTunes
http://support.apple.com/kb/HT2731
Using your Apple ID for Apple services
http://support.apple.com/kb/HT4895
Frequently asked questions about Apple ID
http://support.apple.com/kb/HT5622
Additionally, your Apple ID may be signed into your child's Messages and FaceTime settings. You can check the settings for Messages and FaceTime on your child's device to sign out of your Apple ID:
On iOS devices, find out which addresses are enabled with FaceTime and iMessage by tapping:
- Settings > Messages > Send & Receive > You can be reached by iMessage at:
- Settings > FaceTime > You can be reached by FaceTime at:
iOS and OS X: Link your phone number and Apple ID for use with FaceTime and iMessage
http://support.apple.com/kb/HT5538
Next, I recommend signing out of iCloud on your daughter's device. You can do this by deleting the iCloud account from her device and then signing in with the new Apple ID:
On your iOS device’s Home screen, go to Settings > iCloud, then at the bottom of the screen, tap Delete Account.
iCloud: Change iCloud feature settings
http://support.apple.com/kb/PH2613
Once you delete the account from your device, you will have an option to sign in with your new Apple ID in Settings>iCloud.
Thank you for using Apple Support Communities.
Best,
Sheila M.