Varys leaves next, but when Tyrion starts to go, Tywin won't let him. Tyrion observes, "You just sent the most powerful man in Westeros to bed without his supper." Tywin says he's not the most powerful man in Westeros, which Tyrion obviously knows. Nobody really thinks Joffrey is powerful, except for Joffrey. Tyrion says that armies give power, rather than crowns. Although Robb had armies, and that didn't work out all that great for him. They establish that Walder Frey will get the public credit and blame for Robb's death, although Tyrion knows that Tywin clearly orchestrated the whole thing. Tywin explains that he thinks it's better to kill a dozen people at dinner, rather than ten thousand in battle. I notice he doesn't mention all those Stark soldiers getting massacred out in the camp. Anyway, Tywin did it to end the war and defend the Lannisters. Tyrion thinks that kind of ambush is the sort of thing that the Northerners will never forget, but that doesn't worry Tywin: "Good. Let them remember what happens when they march on the South." I don't know about that. People in the North never seem to worry about the consequences when they decide to do what they think is right.
So! It's time to move on with the plot. The Stark men are dead, and Winterfell is a ruin. Tywin declares that Roose Bolton will be warden of the North until Tyrion's son by Sansa comes of age. And speaking of that, he adds, "I believe you still have some work to do on that score." Tyrion thinks Sansa's not going to be in the mood for love after finding out about her brother and mother, but Tywin doesn't care so much about what kind of mood Sansa is in. I'm pretty sure Tywin has had it with everybody's "moods" and "feelings" and "desires." He wants to just give everybody a list of tasks and have them go away and get them done. Tyrion says, "I will not rape her." Tywin changes the topic slightly and says, "The house that puts family first will always defeat the house that puts the whims and wishes of its sons and daughters first." In other words, get to work. Tyrion says it's easy for Tywin to preach devotion to the family when he's the one who gets to decide what everyone's supposed to do. All the tasks Tywin has to perform just happen to line up with what Tywin wants to do. But when Tywin's asked to name a time that he actually put the family ahead of his own desires, he has an easy answer: "The day that you were born!" He wanted to drown Tyrion, but he let him live and brought him up as his son because he was a Lannister. It's harsh, but it's nice to see Tywin explicitly calling Tyrion a Lannister. Even if he might have been doing it sarcastically, he's still including him in the family.