Apple IDs are designed to be used by one person only. They are not designed to be used as a way to monitor someone else's activities. I suggest that you make your daughter her own Apple ID. Make use of the parental controls available on the iPhone and see what services your carrier offers. There are browsers available in the app store that will allow some additional control.
And, if you find that your daughter is abusing the privilege of having a smart phone, take it away and give her a prepaid flip phone for emergencies. The embarrassment potential alone may give her pause.