Log in errors may be unrelated to the Family Sharing setup.
As a test, if she has any Apple device with the Apple TV app (e.g. iPhone) or computer web browser, then try accessing Apple TV+ content there. That should confirm that the Family Sharing part is working correctly.
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Some other users have also recently mentioned log in errors with select third party devices.
I haven’t seen a broad general resolution here though.
- Please verify that the Fire TV system software is up-to-date.
- Verify that the Apple TV app is up-to-date, if not done automatically.
- Verify that her router or firewall doesn’t block Apple authentication servers, in case she made custom changes.
- Verify that her devices and router use a good DNS, like the one from her ISP, which gets updated with all the server names that Apple might use. Again, only applies if she made custom changes.
- Verify that her Fire TV has the correct date, time, and time zone, as Apple may be more strict about that than other content providers (for TLS secure connection reasons).
Else I would suggest to (have her) contact an expert from the Apple Support staff for further assistance. Contact Apple for support and service (phone numbers) or start your support request online (chat/email/callback).
She is getting an error message
What does it say exactly?