Problem with daughter’s shared name and avatar photo appearing on other phones

So, our continued annoyance with everyone in my family being under one Apple ID has a new problem. Right now, there are 4 of us in the family who share my Apple ID. We each have our own phones, phone numbers, iMessage emails, etc.

However, my daughter, sometime recently, created her own emoticon to display in iMessage. However, when my son or wife texts ME, the update profile pic and name message constantly pops up. My wife was informed by her boss, today, that any texts my wife sends to her ALSO shows the update notice for my daughter’s avatar and name!

I followed the directions to update/remove her avatar, but when I go to the “...” in the primary iMessage window, I get the “Sharing name and photo not available” because multiple phone numbers are associated with our ID. So I now can’t even turn it off!

How did she even manage to update her profile if this message comes up? And why the heck is it sending out from other phones on our account??

UPDATE: For whatever reason, the ability to edit the name and photo was ACTIVE on my wife’s phone, which had my daughter’s name and avatar active to share. I turned it off, but why was it working on her phone and not the others, giving me the error above? Also, no idea why or how my wife’s contact info and photo would have my daughter’s on it. This is infinitely confusing. One of the many reasons Apple ID accounts are a giant headache.