apple tv +

Yes. You can use Family Sharing to share the Apple TV+ subscription with up to 5 other people with different Apple IDs, or just log in with her Apple ID in the living room TV's or streaming device's Apple TV App.

click here ➜ Add a family member to your shared subscriptions - Apple Support

If devices in both rooms have access to their own Apple TV app, then yes, a limited number of simultaneous streams are permitted per subscription.