Can Apple TV be shared with adult family members in different households. One of my family members can use Apple TV on her phone or computer but cannot get it to load on her television

Can Apple TV be shared with adult family members in different households.

Yes, Apple Family Sharing allows users to form a sharing group with members anywhere within the same country (with accounts set for the same country). Every group member uses their own Apple ID account for access to the shared services.

Apple TV+ allows up to 6 simultaneous streams, so for a group of 6 members that would be no more that one stream per user, else you’re blocking each other.

One of my family members can use Apple TV on her phone or computer but cannot get it to load on her television

What kind of television? Does this TV support the Apple TV app? Or does it have a streaming device, that supports the Apple TV app, connected to the TV? Were they able to sign in to the Apple TV app on their TV or other device, through the in-app Settings (sprockets wheel icon), using the Apple ID account as used to the Family Sharing group participation?

List of Apple TV app-supported devices - Apple

Get the Apple TV app or Apple TV+ app on your smart TV or streaming device - Apple Support

All the ways to watch Apple TV+ - Apple Support