It's actually kind of impressive the way almost everything Tywin says to his children is hypocritical (spoilers extended)
Just off the top of my head ;
- He tells Tyrion that Jaime never would have taken his helmet off in battle (Jaime actually rode into battle without his helmet, which was how Cat recognized him in the whispering woods).
- He tells Tyrion Jaime would never have so meekly submitted to capture, right before Jaime is captured by a teenager.
- He tells Tyrion that when men lack discipline the fault lies with their commander, then later also tells Tyrion that Elia's death wasn't his fault because he didn't know what Gregor was going to do.
- He tells Tyrion he wouldn't have ordered a woman raped when he literally ordered Tyrion's wife gang-raped.
- The whoring thing.
- Giving Shae the Hand's chain to wear in bed after he made such a fuss about his father giving his mistress their mother's jewels.
- He was furious about Jaime joining the Kingsguard, even though he spent most of his life as Aerys personal ball-washer. Even after Aerys insulted him, his children, his wife--might have even raped his wife.
- He tells Cersei it's her duty to marry again for their House, but he himself never married again after his first wife died.
- He also clearly married his cousin for love, disrupting helpful alliances in the process.
- He scoffs at Cersei commanding him to come back to defend King's Landing from Stannis in ACoK, only to spend most of the novel sitting in Harrenhal with his finger up his ass, lose an engagement with Edmure, then march Hell-bent for King's Landing to defend the city from Stannis like Cersei told him to in the beginning. Then he throws himself a special ceremony to commemorate his military genius.
- When Tyrion asks him for that same sort of commemoration he says he was only doing his duty and shouldn't expect a reward.
- He tells Joffrey that when somebody defies you, you serve them fire and steel, but when they kneel you should help them back up. He himself is famous for having wiped out most of the families who defy him.
- He calls Ice ridiculous for being too large, but then the sword he designs is so gaudy Brienne can't even wear it openly.
Anyway, here's me summoning a thousand Tywin Lannister dick-riders into the comments to explain how none of these are really hypocritical
