Why not just animate the Hotspot's position as well? Alternatively, you could add a Moveable script to it, and then use the Object: Transform Action to move it through Actions.
Add a RememberTransform script to it, and it's position will be stored in saved games too.
Comments
Is the door physically moving or just animating? If you can provide screenshots or more detail, then it will be more possible to advise.
Add a RememberTransform script to it, and it's position will be stored in saved games too.