Tywin was a can when it came to his own family. He threw his weight around,but in the end they just fucked him up,and never did anything he told them to do anymore. Cersei didnt marry Loras,and Tyrion didnt consummate his marriage to Sansa. Cersei and Jamie fucked all the time,and Jamie stayed on kingsguard duty despite Tywin wanting him back at Casterly Rock. Maybe if he actually loved his fuckin kids they wouldnt need to be doing all this shit,but he didnt,and you can only kick a dog so much before it bits and Tyrion shot that dude with a motherfucking crossbow. Tyrion was smarter,and a nicer person and thats why he is alive and Tywin is dead.
Uh, I know the story of the Lannisters, nothing in your post really has anything to do with Tywin not knowing about Tyrion's whore cave or not wanting Tyrion, as the Hand of the King, whoring around King's Landing.
You are blaming Cersei's & Jaimie's incest on Tywin being a cold father?? That is a little extreme to believe, then again so is that Cersei & Jaimie were able to keep their affair secret for so many years at Casterly Rock and King's Landing (so much for those little birds)..
Perhaps Tyrion is smarter than Tywin, after all, Tywin didn't have the foresight to follow through with his thoughts of drowning Tyrion at birth. And then Tywin moved to war to get Tyrion back when Cat Stark kidnapped the Imp.
Tywin is dead because Tyrion is willing to kill his kin while Tywin was not.
Yes, Tywin is dead but his commentary on Tyrion is proving true so far, "[Tyrion] is low cunning."
Tyrion managed to get outsmarted and framed for murder by a whore, picked a hot headed fool for his champion, murdered the aforementioned whore in a pitiful fit of rage and then killed his own father and thus almost certainly turned Jaimie against him until one of them dies.
Now his pride and arrogance have decimated Dany's forces. His plan got the Ironcans burned, the sand snakes killed/captured and stranded the Dothraki horde on Dragonstone.
His contempt for his father and greed for Casterly Rock netted him another burned naval fleet, unsullied stranded in an empty castle and the loss of Highgarden.
Although, Casterly Rock being empty of gold is absurd. That plot line is ridiculous, no way all the Lannister's mines are dry, especially for years. That would mean thousands of people no longer working in various occupations, towns becoming ghost towns and no one realizes this? The Army of the North didn't find this out when they captured areas of the Westerlands?
If the mines ran dry 3 years ago, why would Tywin have been covering the crown's debts, loaning money to it? No actions to safeguard what remained of his family's wealth, I mean a mines just don't go empty in a day, production slows down not vanishing in a flash across an entire region. Not to mention that no more working gold mine doesn't mean no money; Tywin just went ahead and spent all their money while knowing little else was coming in?
It was a poorly constructed plot line that should have been left out, it was not needed to show that the Iron Throne's debt is separate from House Lannister's finances. Now the richest family in the kingdoms is really broke.
