The same Tywin that has a song on how he will absolutely slaughter his allies. Has a incestuous daughter, a kingslayer son and another genetic abhorrence son? Even if he will have some loyal lords left, no one outside of Lannister will support them since they are already too powerful for the current houses to leave in the status quo. The Tyrells are very unlikely to favour Tywin as well. Robert himself is genuinely popular, especially compared to what came before him.
A lot of houses hated Robert, and he knew it. He even complained about it to Ned, how many lords call him a usurper behind his back. Hence why Robert needed the help of the Arryns, Tullys, and Starks to hold the throne. As for the houses like the Tyrells, they don't need to like the Lannisters; they're more likely willing to just work together for a common cause against a house they see as a usurper.
Especially since they do remember the days when Tywin ran the realm in Aerys' name, and those were some prosperous years of peace. Tywin was already running things back when Stannis and Robert were still kids, and the realm was prosperous back then. So if Robert just kills Cersei and Tywin declares war in response, the latter can count on more than several houses' support.
Stannis himself had this to say about Tywin, and Stannis is an enemy of Tywin's:
"I remember the first time my father took me to court, Robert had to hold my hand. I could not have been older than four, which would have made him five or six. We agreed afterward that the king had been as noble as the dragons were fearsome. Years later, our father told us that Aerys had cut himself on the throne that morning, so his Hand had taken his place. It was Tywin Lannister who'd so impressed us."
-A Storm of Swords, Chapter 54, Davos V
If even his enemies had such high praise for him, imagine the average lordling's view of Tywin, when they remember how good things were back then when he was running the country. Especially considering the fact that the Reynes rebelling against their liege lord gets many lords to see them as the bad guys, seeing Tywin as right for crushing them because they defied the chain of command, and as for the Dornish, most Westerosi lords weren't fond of them either, especially since they fought Dorne for centuries, and the Dornish had a completely different culture when compared to the rest of Westeros.
No fucking way any of the Targaryen will become kings. Heck, they need to be insane to think this isn't a trap to kill them. The only house that somewhat likes them is the sand nigger house.
Most of the noble houses hate each other, but they're more than willing to work with each other for the sake of power. That, and Viserys and Daenerys are kind of desperate. Viserys before Khal Drogo killed him was desperate for a chance to take control, hence why he stole the dragon eggs. One egg to buy a ship, and two eggs to buy a really big army. And Daenerys after Khal Drogo died was left wandering the desert with little hope. If the "King" of Qarth didn't let her in, she would've likely starved to death with her entourage.
Either one of these Targs would react to Tywin offering them the throne by taking the chance. Yes, it could be a trap, but it's better than wasting away in the desert.
Although if it did come to a war between the Baratheons and the Lannisters, the Dornish would side against the Lannisters and probably join the Starks, just so they'd have an excuse to kill Gregor Clegane and Tywin Lannister.
Robert could have killed Cersei and in a fit of rage, the kids too. He never liked Tywin and hated that he offered him Cersei, so he felt stuck with this family, including kids that didn't even look like him. This was Ned's biggest fear and it was a possibility. Killing Cersei and the kids wouldn't have proven her betrayal, only that Robert believed the accusation. It would have made Tywin mad, though.
Robert already hated the bitch. That, and he does have his moments of clarity now and then. He'd know that challenging Tywin to a war would mean the splintering of his fragile realm. Yes, it could probably lead to a war if Robert acts on his impulses and kills Cersei, but the soldier in him would know the logic of having a war with Tywin Lannister, and it'd be bad. Especially since he already complained to Ned that many still call him a usurper, and they'd happily join Tywin's side if the latter rebels. Especially since Tywin ran the realm better than Aerys or Robert ever did, so there'd be a reason for would-be rebels to join Tywin.
The way I see it, Robert would get ultra mad, but the soldier and pragmatist in him (the side that told him Dany was a threat with all those Dothraki by her husband's side) would know that a war with Lannister would be a bad idea now that a Targaryen girl has 40,000 Dothraki screamers at her husband's back, so he'd react to it by exiling Cersei and her children, and then bringing in Stannis' daughter Shireen to marry Robb Stark, Ned's elder son. That way, there'd be a Baratheon and a Stark set to inherit the throne in the odd case he croaks.
OTOH, there is no way Tywin would let the power slip through his fingers like this. He would call the accusations lies and say this is a plot to replace Cersei. He wouldn't give her up to them and he would double down on her innocence, not out of love but because the kids are his only way to get power once Robert was gone.
He might. It depends on how much Cersei's innocence holds up in the eyes of the aristocracy. He could plan to marry a relative of his to the future children of Robb and Shireen. That, or marry in with the Tyrells to build up his own power base and make sure Robb Stark would depend on his side for grain and gold, and he'd have a massive army of 140,000 men close to the capital in case Robb became disagreeable.
We've seen the ending. HBO gave us the canon ending for the main cast right from GRRM's notes. The stuff from the books we didn't see are the inconsequential characters like Euron, Victarion, Quaithe, Young Griff, Connington, and so on. Their stories, like most stories in ASOIAF, barely matter. Just like the Others made almost no difference whatsoever.
Even if the next 2-4 main ASOIAF series books are written, even by GRRM himself, they won't change anything compared to the HBO show anyways. We've gotten the 'greatest hits' version of the ending already. Who really wants one with all the filler content other than diehard ASOIAF fans at this point?
GRRM's writing makes Naruto filler look fulfilling by comparison. And with all the story points he left dangling, there's no way in hell he can finish them all with all the projects he's now involved in.
And yes, a lot of the Game of Thrones' ending felt like GRRM's writing. About how absolute monarchs like Daenerys eventually turn bad, how expectations are subverted, how there's no real good guy in war, how everything ends with a slow march to democracy, which is seen as a good thing by the author, hence why electoral monarchy is portrayed as a positive as opposed to absolute monarchy.
The one thing that was running through my head as I saw the last season is how everything lines up with GRRM's negative views on monarchy and religious prophecy, and his tendency to "subvert" expectations was in full view.
