I cheated a bit. I first thought that the music would have to be classical, because of the period in which the story was set. Then I thought maybe an opera piece would be perfect, because they went to the opera a couple of times in the novel. But instead, I looked up the soundtrack for the 1997 Anna Karenina movie on Wikipedia.
That article gave me the perfect piece, which I immediately downloaded on iTunes: Tchaikovshy's Symphony No. 6, "Pathetique". It contains several movements, some with manic allegros reflecting Anna's mood, and then really dark periods of exaggerated tragedy. It's also really long!
Here's a version from YouTube: