Daughter's iCloud image changes mine

It's likely that you are sharing some kind of information piece in your contacts (perhaps a home phone, email address, etc.) Contacts is trying to outsmart you by indicating that the contact might be a duplicate; the same person based on information listed. You can check in contacts to see what shared info exists and erase it. You can also check (I believe at the bottom of the contact card) where it says contact suggested from.... or similar.