Just for fun: if Tywin was in Otto's place for the Dance but with Alicent as his daughter instead of Cersei, how do you think it would have played out?
I think a lot of pre-Dance stuff would play out largely the same, given that there are similarities between Otto and Tywin and how their lives played out and what they wanted. But there's a key difference between them: Otto's very much focused on personal advancement, placing Alicent as an option for queen and Aegon in the line of succession for king is all about how that can help him get as much power as he wants (cuz Second Son Complex I guess), while Tywin is all about family advancement. He has his personal cares and his personal wants, yes, but Tywin's primary focus is on advancing the Lannister name, the Lannister glory, the Lannister agenda. So while yes, Tywin would likely also want Alicent to be made queen, and would want to do whatever possible to make that happen (much like how he was all about getting a grieving Robert to marry Cersei without care to the fact that Robert was the worst man living), it would be all about family for him, about the advancement of the House.
An interesting thing of note is that Tywin is...I don't want to say less manipulative than Otto, but less personally conniving than him. Think about it: we see Tywin primarily through Tyrion's eyes, given that Jaime only gets one or two scenes with Tywin while he's still living, and Cersei none as her POV chapters start when he's already dead. So we're seeing Tywin as a character through the eyes of someone who loathes him, and who he loathes in return, but the image we get is an interesting one. Tywin isn't as overtly hostile in the books as he is in the show, and while he's clearly contemptuous of Tyrion and hates him, he is, in a strange way, able to recognize the virtues Tyrion has, and is able to be honest and frank with him. I mean Hell, Tywin admits to Tyrion, in detail, exactly what his culpability is in Elia's death (rip Elia, every single corner of this fandom does you dirty in so many different ways, I will treat you better Queen). And that's with a kid he hates.
So with a kid like Alicent, someone who's less of a letdown than Jaime, less of a constant source of irritation than Cersei, and less personally despised than Tyrion, Tywin would likely be as close to Alicent as he can be with a child of his. I mean, he's a clear narcissist and misogynist and kind of a shitty person even, but still the best character, and while he might be less openly affectionate than Otto is, we know that Tywin could form personal relationships with deep ties for him, like his love for Joanna and his affection for Kevan (and if I think about Tywin and Kevan for too long I do cry), so he and Alicent likely would be on good enough terms to be in lockstep with each other during the Dance.
How Tywin would play out during the Dance, in Otto's place, is a bit hard to game out, because the show hasn't gotten there yet and we don't know how they're going to play out certain events, but I'll theorize nonetheless while trying to keep within the events in the Fire&Blood canon. For one, Tywin would be more militantly minded than Otto was, though still working just as hard on the diplomatic front, given the cunning genius that he is, so the Greens would get an additional military commander in the field to their advantage. And because Aegon is more inclined to listen to his mother (I'd say that currently he's less trigger happy than his book counterpart too, but that might not last because of What Happened To Aegon happened to me I'd go on a murder spree for a full decade), along with Tywin being a more intimidating force than Otto, Tywin likely wouldn't be dismissed as Hand of the King, leaving Aegon with a great advisor and Tywin with a king who will listen to him and a daughter-queen who will back him up.
Ending it can go one of three ways. Either a) Tywin, as an able military commander himself, goes into the field and is killed in battle, though likely at great cost to the Blacks, b) Tywin is still in King's Landing when Rhaenyra takes over and, like Otto, is beheaded for treason or c) Greens win. If Tywin doesn't die, then he would likely help the Greens emerge victorious. We'd see marriage alliances like we do with the Tyrell marriage and the Martell marriages (given that Jahaera and Maelor can be betrothed though I don't imagine Jahaera getting married in anything but name given that "eight going on four" characterization, and he definitely would take better care keeping them safe, and Daeron's of marriageable age, and I've decided to live in a fantasy world where this means Aemond also lives and Alys gets to be Lady of Harrenhal somehow and Tywin is magically cool with this because that means they get the loyalty of Harrenhal and a great grandson as the future Lord of Harrenhal), back alley deals like with the Red Wedding with sweeteners to get wavering supporters of Rhaenyra's over to his side, and his general ability to get shit done and make them go his way means that the Greens emerge victorious and the Blacks are likely to be roundly defeated, either through out and out death like Robb, or through such a trouncing there's no choice left but exile and disappearance, like they think with Stannis.
I think we should picture that for a minute. Tywin victorious after the Dance, him at the helm of his kingdom with his daughter ready to aid in whatever way she can, Aegon is king and hopefully healing from wounds, he and Helaena start to heal and focus on raising Jahaera and Maelor, Aemond's there with his wife, Lady Alys of Harrenhal and their son, Daeron off doing whatever he does (likely after being fostered at Casterly Rock/Lannisport instead of Oldtown), Criston’s watching over them all in peak guardian stance, alliances strong, marriage pacts brokered, kingdoms being restored, Hell I'll even throw in Aegon the Younger as a nicely kept hostage for good behavior with a betrothal to Daenaera Velaryon in the future, cuz this is my happy ending with Tywin as de-facto god emperor of the world and I want it.
