Recently I purchased my own copy of Russian Ark; I'd seen it just once and not absorbed it very well.
Now that I can watch it at my leisure I can appreciate it much more than before. As many already have indicated, the film has a dreamlike tone and is meant to show you the treasures of the Hermitage and the Hermitage itself, while at the same time reminding you of the Hermitage's place in Russian history. If you accept this approach, then you will not be disappointed in the very brief depictions of Alexandra, her sister Elizabeth, Nicholas, and the children. As many of you have noted, they are taking tea in the room at the end of a long hallway where the Provisional Government made its last stand; the filmmakers are going for symbolism rather than reality. As for the four young girls who run down the hallway with Anastasia, I believe the filmmakers intended that brief scene to foreshadow the Anastasia mythology of her supposed separation from her family.