On appleid.apple.com, go to Devices then select a device. Read the details of the device and then remove it from your account. Read the warning that appears. To confirm removal, click again.
Click Remove to remove a device. If you can’t remove a device, log out of your Apple ID on it and try again. If you still can’t get rid of it,
The simple answer is no deleting an old iPhone backup from iCloud will not affect any of the data on your real iPhone. To remove any device backup stored in iCloud, go to your iOS Settings app and select iCloud, Storage & Backup, then Manage Storage.
Your music, photos, apps, and other data will not be deleted if you cancel your daughter’s cellphone contract. You’ll just need to establish your own cellular account with the provider in order to use the phone outside of the Wi-Fi range. You won’t be able to share her music or applications with others.
The long answer is that you can’t have both. You are the same person when you share an Apple ID, so you’re using two different devices. Your phones are operating as anticipated. If you don’t want to create a new Apple ID, your devices’ capabilities will be restricted.