Change Apple ID on one of two phones sharing an ID
Long question:
Parent's phones. They've been sharing an Apple ID. I have created a new ID for my mom and tried to switch her phone to it but having trouble:
I can change to her new ID in settings>Name & ID>iTunes & App Store, but it's still connected to my dad's phone.
If I try to change the "Reachable At," I get a message that I can't use the email being used for notifications.
If I remove a phone number from "Reachable At" it takes it off of both phones.
#1 - What am I doing wrong? Is there a step I've missed to disconnect the two phones before I try to switch to her new Apple ID?
#2 - If I finally succeed, will she lose her pictures and contacts? I have it backed up to a computer, but if I restore from that back up, won't I just put it back to my dad's Apple ID?
iPhone 7