If you've read that far ahead, you should know that his deal with Tyrion is complicated (and some of the back story is very vague). He is very ruthless, and he's done a lot of bad things without remorse but he's always done them to protect his family. Lannisters do have their own code of honor (A Lannister pays their debts), and it was Joffrey who dragged his family into war not Tywin.
A Song of Ice and Fire is much like the Romance of the Three Kingdoms, and Tywin is Cao Cao. He's a hard and cunning man, but what exactly do you want him to do with his cupbearer, backhand her occasionaly?