Anna Karenina Part 3, Chapters 12-23
Karenin is at his wit's end with his wife's affair and doesn't quite know how to handle knowing that his wife is an adulteress. He considers both challenging Vronsky to a fight and divorcing Anna. He decides against both of those options, going instead with what will be the easiest: pretending in public that everything is fine between him and his wife. He decides that this option will cause Anna the most grief anyway. The guilt will destroy her, Karenin predicts.
"'Alexsey Aleksandrovich! What is it you want of me?"'
"'I want you not to meet that man here, and to conduct yourself so that neither the world nor the servants can reproach you...not to see him. That's not much, I think. And in return you will enjoy all the privileges of a faithful wife without fulfilling her duties. That's all I have to say to you. Now it's time for me to go. I'm not dining at home.' He got up and moved toward the door." Part 3, Chapter 23, pg. 338
Anna agrees with her husband that the best thing to do is indeed to stay together and avoid a public scandal. She goes to Princess Betsy for advice. It doesn't reflect well on Anna that she seeks advice from a gossip queen.
Karenin goes along with his plan to undermine Anna by sending her money, along with a very cool and impersonal note. Vronsky, too, is having problems. His career isn't advancing as quickly as he wants it to. He heard from an old friend that women are the obstacles to a man's career advancement. With that, Vronsky begins to worry that Anna is getting in the way of his own success. And if he can't be successful, their love is doomed anyway.