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If you dislike Tywin Lannister, then this is a fun chapter for you. After realizing that he was tricked, Tywin starts moving his army, he runs into bad news: Jaime is captured and all of Jaime's army was basically destroyed, so Riverrun is free.
On top of that, Robert's younger brother Stannis seems to be gathering an army at his castle, Dragonstone; and Robert's youngest brother Renly married into the powerful Tyrell family and is gathering an army in the south.
So Tywin may be caught between three enemy armies. (And since Joffrey killed Eddard, Tywin has no leverage over the Starks.)
Although Tywin never seemed to like Tyrion, he decides to send him to King's Landing to act as the Hand of the King because Cersei and Joffrey have messed up so much.
But Tywin doesn't want Tyrion to bring Shae to court. Who will Tyrion side with: the father that never liked him or the woman he's sleeping with?