Is this about the Apple TV app or about the Apple TV set-top box?
If this is about the Apple TV app on another device, then which device (instead of mentioned iPad)?
When you have Family Sharing activated with additionally Purchase Sharing, then you can share bought movies from the iTunes Store. Verify that the (currently active) Apple ID account on Apple TV is one of the accounts in Family Sharing.
Family Sharing without purchase sharing won’t allow access to family member’s purchases.
The Apple TV box cannot download any movie. It is a streaming device.
Share App Store, iTunes Store, and Apple Books purchases with Family Sharing - Apple Support
If there's an issue when you redownload apps, movies, or other content from Apple - Apple Support
If you don't see your family's shared content - Apple Support
You start shared movies from the Purchased tab, then select the family member, then select from their content.