Yes, Tywin was impressive in some ways. He was intelligent, diligent and hardworking, a a good politician and hellbent on having control over everything, which meant that under his rule house Lannister rose in station. He was also a dismally cruel man, a petty, bitter person, a moral coward whose elitism and brutal methods exceeded by far the norm among the nobles of his times. He focused on getting his children, specially Cersei and Jaime, powerful position because that was what he saw them primarily, tools to his own goals, but his neglect of giving them a moral guidance and genuine affection helped to turn them into the messy, reviled creatures they are now and tainted house Lannister's honor like never before in the history, after Aegon's conquest. So that is Tywin. A despicable person who was also capable of acquiring more wealth and power than was already given to him in his cradle. You can be a failure as a father and as a human being while still being wealthy and powerful.
That doesn't make Cersei's achievements really impressive. She got a small council after she murdered the king and ruled through his children. When Tommen wants to exercise his authority she bullies him. That is her approach. Make sure people fear her and use daddy's influence to fulfill her desires. Once daddy is dead she goes on to screw everything for her family.
Compare that to Queen Alysanne, the example you refused to acknowledge as a major counterpoint for Cersei. The good queen changed paradigms, showed true competency and compassion and actually did good to the people of the realm.
Littlefinger has an interesting take on Cersei. He is a liar but he has no reason to lie in this occasion and his analysis is quite precise.
“Yes, but don’t let that trouble you. You’re still half a child. Every man’s a piece to start with, and every maid as well. Even some who think they are players.” He ate another seed. “Cersei, for one. She thinks herself sly, but in truth she is utterly predictable. Her strength rests on her beauty, birth, and riches. Only the first of those is truly her own, and it will soon desert her. I pity her then. She wants power, but has no notion what to do with it when she gets it. Everyone wants something, Alayne. And when you know what a man wants you know who he is, and how to move him.”
I'm not ignoring my previous argument. I never said Tywin didn't want other Lannister's as partners in life. I said he as the leader of his house and older brother wanted one of his sons to inherent his riches and power and that Jaime rejecting everything he planned was a major strike on his ego. With that said I mentioned from the beginning that Jaime's decision over this matter hardly means he was a failure in my opinion. He is a failure because he is called Kingslayer for having murdered the first king he served, committed treason against the next one and plunged the realm in a war and finally is reduced to guarding his son, a bastard he can never acknowledge who should never be on the throne and whose kingship is a mockery of the very laws that guarantee Jaime's position in society. Jaime is trying his hardest not to be forever remembered as an oathbreaker and the Kingslayer but in the current state of things this still seems much more likely than Goldenhand the Just. With that said, Tywin still doesn't think a Lord Commander of the Kingsguard was a great achievement for his son seeing how he tried the best for having him resigned, how he was furious when Jaime joined the brotherhood in the first place and how Aerys used it to spite Tywin and finally how he disowned his son after Jaime refused to be anything else than Lord Commander.
If Tywin felt he had the same obligations his children had in his eyes he would have remarried and brought new alliances. He still thought he could have used his children/ tools to continue his legacy. Do you really think Tywin would be OK with Lancel or another one of his brother's or cousin's children inheriting Casterly Rock? Why he disowned Jaime over his refusal to marry? It was not a trivial thing for him. Tywin has a massive ego.
No, it doesn't. It proves Tywin regarded Tyrion as a fool until this moment. If he bothered to have the minimal interest in his son's intellectual life he would know he was a scholar and well versed in lot of things, including politics. But, no. Only after years he recognized that he wasn't fit to wear a motley. Tyrion never reminisces about Tywin giving support him in anything. It was always about bringing him down. Tyrion remembers Gerion praising him for memorizing the seven wonders but not a mention about Tywin's approval is made. In fact, later on this happens:
Lord Tywin had put an end to that hope ten days before his dwarf son’s sixteenth nameday, when Tyrion asked to tour the Nine Free Cities, as his uncles had done at that same age. “My brothers could be relied upon to bring no shame upon House Lannister,” his father had replied. “Neither ever wed a whore.” And when Tyrion had reminded him that in ten days he would be a man grown, free to travel where he wished, Lord Tywin had said, “No man is free. Only children and fools think elsewise. Go, by all means. Wear motley and stand upon your head to amuse the spice lords and the cheese kings. Just see that you pay your own way and put aside any thoughts of returning.” At that the boy’s defiance had crumbled.
Is that encouraging his son to seek knowledge?
Later he gives Tyrion an occupation, a rather shitty one. Reminds me a bit of Roose giving Reek as a present to Ramsay and his mother.
“If it is useful occupation you require, useful occupation you shall have,” his father then said. So to mark his manhood, Tyrion was given charge of all the drains and cisterns within Casterly Rock. Perhaps he hoped I’d fall into one. But Tywin had been disappointed in that. The drains never drained half so well as when he had charge of them.
Perhaps he hoped I’d fall into one. I wonder how he got this notion...
He did not hate him? He spent half a year without speaking to Genna after she said Tyrion was more like him that Jaime.
When you have a conversation like that with your son, do you think there is some level of affection involved in their relationship?
Lord Tywin’s eyes were a pale green flecked with gold, as luminous as they were merciless. “Casterly Rock,” he declared in a flat cold dead tone. And then, “Never.”
The word hung between them, huge, sharp, poisoned.
I knew the answer before I asked, Tyrion said. Eighteen years since Jaime joined the Kingsguard, and I never once raised the issue. I must have known. I must always have known. “Why?” he made himself ask, though he knew he would rue the question.
“You ask that? You, who killed your mother to come into the world? You are an ill-made, devious, disobedient, spiteful little creature full of envy, lust, and low cunning. Men’s laws give you the right to bear my name and display my colors, since I cannot prove that you are not mine. To teach me humility, the gods have condemned me to watch you waddle about wearing that proud lion that was my father’s sigil and his father’s before him. But neither gods nor men shall ever compel me to let you turn Casterly Rock into your whorehouse.”
Sure, that doesn't show hate at all.
Do you need more proof than that?
But, of course, Hoster didn't attend two of Walder's wedding and gave him a nickname. That proves Hoster treated his bannerman like shit. Or maybe it's just that you like Walder and Tywin and can't have a unbiased opinion about them.
Yes, he recognized Tyrion has a low cunning later on and he keeps him in a powerful position while still calling him a fool and a person who brought shame to house Lannister in occasions.
I never said he wanted Tyrion to act like a fool. That would ridicule house Lannister and himself in the eyes of others and his ego can't afford that. Still, it's clear he was simultaneously neglectful and abusive in his relationship with Tyrion and never valued his intellect until very later on. Of course later he still took the time to throw a spectacular pile of insults on Tyrion that you can check above. And before he put Tyrion is a ridiculous dangerous situation during the battle of the Green Fork because he would not share his battle plans with a person who associates with savages.
Do you think Tyrion's resentment is gratuitous?
He was not "a very great father". Are you kidding me? A father who put his son through a situation where he is sexually and emotionally abused while torturing his wife in a horrifying fashion is not great? Tell me about euphemism! He is one of the worst fathers depicted in the story. It's mind boggling actually.
And you say we have no idea how they interacted before that scene in AGOT? Well, that should give you a pretty clear picture.