Share/send a link to a movie or show using Apple TV

There is a Share button on mobile (iPhone, iPad) and desktop (Mac) for all iTunes Store content in the TV app or iTunes Store app or iTunes application. From the Share function, choose Copy link, or send directly through Messages, email, WhatsApp, or other supported communication.

I think that might bring the functionality that you seek?

For Apple iTunes Store movie titles, each user should have their own access to that title. You can’t share it with just anybody in another location, but you can buy it for her as a gift. Gift apps, music, movies, and more from Apple - Apple Support.

Likewise, if both users have Disney+, then you both may access any title available on there as included with the standard plan. You can’t share it if only one of the users has this subscription service.

When both users have access to a title from Apple, then both users can watch a title at the same time through Apple SharePlay.

Use SharePlay to watch, listen, and play together in FaceTime on iPhone - Apple Support

Once the FaceTime ‘connection’ for this is set up, then both users can ‘transfer’ it to their Apple TV box.

(Disney+ has ‘GroupWatch’ to watch content together in two locations, when both are subscribers.)

If you are both in the same Family Sharing group, with Purchase Sharing active (=organizer pays for all), only then can you share Apple movie purchases within that group.