Levin's hope regarding his relationship with Kitty begins to resurface.
Dolly explains that Levin has to take action again: sometimes when a man asks a woman to marry, she's just not ready to accept him.
What it boils down to is that Dolly thinks Kitty's refusal of Levin means nothing.
Levin is angry that Dolly is reviving his hope: he doesn't want to be crushed again.
Tanya comes in and asks her mother about a spade.
Dolly insists on speaking French to her daughter.
(Just a note: dating from the 18th century, and even after the Napoleonic wars with Russia in the early 19th century, French was the language of the Czarist Court. Russian remained the language of everyday life, but French, especially among the nobility, was the language of intellectual and philosophical achievement. See LanguageHat on a discussion of French versus Russian in Tolstoy's other giant novel, War and Peace.)
Levin, observing the whole episode, is irritated. He thinks that teaching Russian children French "unteaches" them sincerity.
Levin can't know that Dolly has thought over this problem twenty times over, and has decided that it is more important for her children to know French.
After tea, Dolly too is no longer cheerful. Tanya and Grisha had a fight about a ball. She feels that her children are not charming, but instead bad and ill-bred.
Levin tries to soothe Dolly, but he inwardly blames her decision to talk to her children in French for their bad behavior. He thinks to himself that he will never have such spoiled children: he will allow them to behave naturally.