How can I avoid double charges for purchased movies in Family Sharing?

To access Family Sharing content, the Purchase Sharing option should be activated in Family Sharing settings.

To access Family Sharing content, the others should navigate to their own Library, then Family Sharing, then You, and then the shared movies would be listed. It won’t be accessible as shared from Search or Store.

P.S. If one of the family group members buys it on their own account, with your permission, then you would be billed as organizer, but then they can access it directly on their own account. This could keep your own Library cleaner, less cluttered with fluff that might not be of interest to yourself (e.g. kids movie).

How to share apps and purchases with your family - Apple Support

If you can't find your family's shared apps and content - Apple Support

Note that rented movies cannot be shared through Family Sharing. Purchase Sharing is about buy-content.

How are they trying to watch it exactly?

Did you actually buy the movie or did you just rent it?

To access family shared purchases, family members must go through the purchase history, not the entry in the TV app directly.

click here ➜ How to download apps and content that your family members purchased - Apple Support

Movie Rentals cannot be shared.