Unlink Apple ID from my Apple ID

I am guessing she used to use your ID on her phone. If that is true, you were working intrinsically against how Apple has designed the system to work. Since it was using your ID then according to Apple it was "your" phone. She should have done everything in this document before signing in with her own account --> What to do before you sell, give away, or trade in your iPhone or iPad - Apple Support

If she does not want to delete everything then you are going to have to learn all the details of what to do in this situation. At least remove your ID from Find My, and have her delete all the apps which were installed when your ID was on the device. She will need to download them with her account or get them under Family Sharing. Set up Family Sharing - Apple Support

Apple IDs are not connected to each other in any way.

It sounds like she is using a backup that contains media or apps that are still tied to your Apple ID to set up her new devices.

If at any point apps or movies or tv shows were downloaded on her devices with your Apple ID, those remain tied to it forever and in the case of Apps will forever require it and its password to download and update.

The only way to resolve this, is to find the content, media and apps that is still tied to your Apple ID and delete them from her devices so future backups and devices don't require your password anymore.

What devices is she she setting up? If she is signing into a device with her account then it will require her password. I suspect I am missing some tiny clue which would point to what is happening because other than Family Sharing and limited control by Parental Controls, there is no linking of Apple IDs. Typically a request for another account's password is when a person has apps downloaded with a different account on their device.