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and the Tyrells. He needs them both to keep peace. And with Mercella married into the Martell family and their basically having her as a hostage he rather has to make nice with them. He's a lot more put out that it wasn't Doran Martell that came to the wedding since he's the prince, and Oberyn is just the second son... but Oberyn is the dangerous one, and this Tywin also knows. Oberyn coming in Doran's place was the far far bigger insult, but it was also rather a threat, hence Tywin having to keep his cool even more. And, of course, this Oberyn also knows and is enjoying it using every little opportunity to step on Lannister toes a bit.

Tywin doesn't give a rat's butt about Tyrion, which has been pretty clear in past episodes. Soon we'll see just how hostile he is toward this son he always hated. He even said he'd never have accepted him if he could have found a way to put his ancestry on some other man other than him. He considers Tyrion to be a huge slight on his manhood not to mention his ego. He also doesn't realize that part of why he hates him is that Tyrion is the most like him of all his children. But also Tywin doesn't really love any of his children. To him they're merely assets to use for his own self interest. Tyrion constantly throws that in his face though Cercei also did once last season.

Tywin is actually far more of a shit than Joffrey could have ever hoped to be. But Tywin is also controlled, logical and very clever. He's by far the biggest viper of them all.