How do I remove my messages from my child's mac with family sharing?

If you are sharing an Apple ID, you might consider getting your child their own Apple ID so your data doesn't get shared. If Messages is the only problem, you can use the new ID only for Messages/FaceTime.

If 13 years old or older.

Apple ID - create a new.      

Apple ID – Create         

If under 13 years old, you will need to set up Family Sharing to create an ID.

Family Sharing and Apple ID for your child.      

Family Sharing.         

Family Sharing - Set up.