That's irrelevant when discussing one war specifically. And we were discussing the War of the Five Kings. You know... the only war he actually fought in during the series? It wasn't him that sowed future trouble, it's the fact that Cersei was an incompetent and delusional moron that had no idea how to run the kingdom. Tywin's plan was to have Cersei sent back to Casterly Rock so she couldn't screw up things in the capital and negatively influence Tommen. Since this didn't happen because of his unexpected death, and because Cersei was astoundingly stupid and refused all good advice given to her, things went badly. None of that is on Tywin.
A lot of wars throughout history have been grouped under one larger name because they took place at the same time, in roughly the same region, and shared some of the same combatants. Should we go back through history and start renaming every war that's like this? Should we change the names of the World Wars and break them down into half a dozen separate wars, even though almost all of them involve several of the same parties and began from the same casus belli? The Napoleonic Wars? The Revolutionary Wars? The American War of Independence? The Seven Years' War? The War of the Austrian Succession? The Great Northern War? The War of the Spanish Succession? The Nine Years' War? The Thirty Years' War? I could keep going, but I'll limit it to only modern history.
Or maybe rather than being a contrarian for contrarian's sake, you can just leave it be because that's how everyone refers to it. It's how George R.R. Martin refers to it too. Doing this type of mental gymnastics to prove some extremely vague and trivial point seems pointless.
But it doesn't. Sansa's escape doesn't motivate the remnants of Robb's "kingdom" to keep fighting - the only sources of continued resistance where in the riverlands - at Riverrun and Raventree - and this had nothing to do with Sansa, since their resistance had begun before Sansa escaped, and it ended without anyone knowing anything about Sansa. If there's any future fighting that involves Sansa, it will be a separate conflict, not a continuation of the War of the Five Kings, since none of the said five kings will be involved.
Against none of the original combatants of the War of the Five Kings, in a theatre vastly separated from the rest. I think that disqualifies it as being considered part of the War of the Five Kings. Westerosi law and customs ends at the Wall, and Mance was king beyond it. He was not relevant to the War of the Five Kings, he was relevant to separate conflicts. Just because they take place on the same continent (which is the size of South America) doesn't mean it's the same war, and the war in question was called the War of the FIVE Kings, and those five kings were clearly listed, and none of them was Mance. The major foundational factor in the War of the Five Kings was that it began as a war between the Starks and the Lannisters, and the other theatres and campaigns of that war were caused because of this (e.g. Stannis, Renly, Balon). But that isn't the case with Mance. He was already doing what he was doing long before the war started, and he did not come into contact with either the Starks, the Lannisters, or any of their allies.
tl;dr: The conflict at and beyond the Wall was not connected to the War of the Five Kings.
This falls clearly into the "Aftermath of the war" category of things. Subsequent guerilla violence in individual regions that were affected by a war does not mean it's a direct continuation of the war. Partisan and guerilla violence continued in the Baltic states after WW2 ended, which the Soviets took several years to brutally stamp out, but we don't consider World War II to have continued to 1956, do we?
But he didn't want nor need said alliance. He preferred having the North be ruled by an actual Northern house, as morally questionable as they were. There was a small chance of pacifying the North through a Bolton puppet regime - there was NO chance under continued foreign occupation by the ironborn.
I made somewhat of a mistake by saying Tywin would choose only one or the other, since as @Minsc said, Tywin was essentially using the Boltons to do the hard work of putting everyone in the North back in line, so by the time Tyrion and Sansa went north they'd have a relatively stable region to rule over. The Boltons weren't going to be removed - Roose was still going to be Warden of the North, as Tywin believed he'd be more competent and palatable to northerners than Tyrion, and Ramsay was still going to marry "Arya" - but since Tyrion would be married to the actual heir to Winterfell, that'd trump all the rest, legally speaking. But it wouldn't hurt to have two allies in the North - the Tyrion-Sansa one, and the Roose-Ramsay-fArya one. Roose only took possession of Winterfell in Dance, long after the Tyrion-Sansa plan fell through.
Still better than if Tywin allied with the ironborn and let them have free reign to pillage all of the North.
But when did Tywin said this? As I recall, it was fairly early in Storm, during one of Tyrion's first chapters, and the first Small Council meeting that he attends. It might have been before Tywin and Roose formed their conspiracy to dominate the North themselves.
In all likelihood they were about to, though. But they didn't, because guess why? Tywin and the Reach lords arrived.
Yeah, so? I'm not denying that he fought bravely and well, and that he contributed to the city holding out a little longer, but he still hadn't won the battle and saved the city. All he'd done was delay Stannis's attack.
It has citations to the specific chapter where said information is revealed, which is its main use.
He stopped the King's Gate from being breached, but not the Mud Gate - the one closest to the river - and he also hadn't stopped the mobs about to break through two other gates on the other side of the city. The gold cloak defenders had fled from these gates, and they were completely unprotected and vulnerable. If Tywin and the reinforcements hadn't have arrived, they would have fallen pretty soon.
I'm not sure why you're arguing this specific point. It's very clearly stated in the books that the battle seemed to be lost and that the city's defenses had failed. Gates and walls are useless if there's no one on them to defend them.
The book states several times that there was soldiers attacking the Mud Gate, which is on the northern bank of the Blackwater Rush. It doesn't matter if the "main force" wasn't across, all it would take is a small handful of soldiers to breach the gate, since again, THE GOLD CLOAK DEFENDERS HAD FLED. Even just one open gate would let the entirety of Stannis's army pour into the undefended and chaotic city.
And why did they lose?
Oh, because Tywin and the reinforcements arrived to destroy them before they opened the gates, which they were poised to do any moment?
I'm just.... I'm so confused by what you're trying to argue here. These problems weren't removed by Tyrion. While the Mud Gate was being attacked and the other two gates were being swarmed by mobs, Tyrion was lying with his face cut open on the bridge of boats. He had nothing to do with defending those other gates. He successfully defended the King's Gate, yes, but not the other three. Why is this concept so hard to understand?
He sent Baelish to attempt to negotiate an alliance, but that isn't the same as "ordering reinforcements" to arrive at a specific time.
"Like always"? So why did he sit at Harrenhal for a few months after the Battle of the Green Fork, rather than marching on Robb's host at once?
Tywin only marched west after:
The Battle of Oxcross saw an entire Lannister army destroyed, and
Renly was killed, his vast host scattered, and Stannis was stuck outside Storm's End
Because of these things, the westerlands were completely undefended, and there was no immediate threat to the east because EVERYONE expected Stannis to be stuck besieging Storm's End for the foreseeable future. No one expected he'd deus ex machina his way to instant victory with a shadowbaby demon.
Tywin's decision to march west at this point was completely strategically sound based on all of the information that he had. You can't judge his decisions with the hindsight and knowledge of the rest of the book and all the other PoV storylines. That's not how commanders make strategic decisions.
What does this even mean? Tywin didn't delay in anything. After his forces were beaten by Edmure's at the Battle of the Fords, he turns and marches south-east instead, where he meets up with Lords Rowan and Tarly, and they then meet up with Mace Tyrell. Tywin rendezvoused with the Reach reinforcements as soon as possible.
What, you mean that Tyrion expected them to arrive specifically while the battle was going on? Really? You're aware of how large Westeros is, right? It's the size of South America, and the distance between the Reach and King's Landing is hundreds of miles. Tyrion had not a single word about the possible Tyrell alliance - aside from a completely unfounded guess at what might have occurred, he had absolutely no idea that an alliance had been formed and that reinforcements were marching rapidly to the city. He had no evidence that suggested that.
Bronn and a couple of KG weren't enough to hold back Stannis's army. They weren't gods or superheroes. Mandon Moore got killed by a bloody kid.
Yeah, and how would that have helped the city during the night of the battle when several gates were about to be breached and the city's defenders on the walls had fled in panic? "A day or two later" would see the wildlings show up outside of a city occupied by Stannis and his army.
But this is actually exactly what Martin was suggesting in the chapters. Lancel staggers in and tells Cersei that the battle is lost, not just because Tyrion has fallen, but because the gold cloaks had mutinied, killed their officers and fled their posts.
Tyrion took the bulk of the trustworthy soldiers with him on his sortie which relieved the King's Gate and fought at the bridge of boats, but they never reached the Mud Gate, which was under direct attack by Stannis's troops. With no one defending the Mud Gate and the other gates, the city was on the verge of being breached by Stannis's troops.
Tyrion only decided to confront Tywin after learning the truth about Tysha. Before that he was set on just getting the hell out of there. It's the show that made it all about his arrest and disinheritance.
But no one said that. They're completely different situations. This is a false equivalency.
With all due respect, I think your reading of him is very flawed and overly biased.
Jealous? About what? Tywin was the one that ruled the Seven Kingdoms in all but name. Hence Ser Illyn Payne's poorly chosen remarks. Tywin never cared much about ceremonial pomp, he was satisfied to just be running things behind the scenes.
So why did he take several actions that damaged his reputation but made his family more powerful, such as the sack of King's Landing, and the brutal campaigns in the riverlands?
At this point you're not even providing evidence for your claims, you're just making sweeping statements about how much you hate a character. It's a fact that because of Tywin's actions, his family became supremely powerful. His oldest son joined the kingsguard, his daughter married the king, his nephew squired for the king, his brothers and other relatives became knights. Later, he saved his grandson's regime - muddying his own name by atrocities in the process - and organised not one but two marriages for his grandsons into the most powerful family in the kingdom. He gave his relatives chances to prove themselves by giving them important commands and posts. He made his nephew Lord of Darry, his sister Lady of Riverrun, even Tyrion, who he personally despised, he was planning on making Lord of Winterfell.
Do I need to keep going?
He left House Lannister in a supremely powerful position by the time he died. Whether you personally like him or approve of his actions or not is irrelevant to the reality of what happened.
He didn't care if people hated him or not. He just wanted them to respect his authority and do as he said. That's not the same as thirsting for glory. Renly and Robert and Robb thirsted for glory. Tywin did not. He just wanted to win, and win decisively.
Because of Cersei and her stupidity.
He was certainly petty and ruthless, but that doesn't mean he was stupid or incompetent. Cersei is someone who's pettiness and ruthlessness were matched by her stupidity and incompetence. She took only half of Tywin's traits. That's... sort of the point of her entire character arc in Feast.
Lions are not dumb beasts, by the way. They're considered the king of the jungle for a reason.
I think we're just going to have to agree to disagree on this issue. We obviously have vastly different interpretations of this character, and have read the series in.... different.... ways.