How to fix Family Sharing issues with Messages and FaceTime?

My daughter used to use an iPad attached to my Apple ID but we bought her an Apple Watch so I logged my Apple ID off the iPad and created her own Apple ID under family sharing to use for the iPad and new watch. Everything went fine except my iMessages and FaceTime still show up on the iPad and her’s do not.

The iPad is logged in under her Apple ID and her phone number and Apple ID are the only ones listed under “Send and Receive” in the iMessage settings.

Help!

[Re-Titled by Moderator]

Original Title: Family sharing problem with messages and facetime