So what if Aerys and Joanna had a secret love child before Joanna was married to Tywin?
Let’s call the child uh Aemon or some other name.
Waters that is.
The child is sent to the Velaryons’s or some other close vassal of the Targs. Mostly to avoid the embarrassment and public scandal, as well as ensure Tywin didn’t find out if the child was raised in KL(I’m guessing the child is sent away months at most from Tywin and Joanna marrying).
Once Tywin and Joanna are wedded and bedded-Tywin finds out about his wife’s history as Aerys’ paramour. He can’t really do much about this but it sets his pride against Aerys.
It does make him a lot more suspicious and less “in love” with his wife. So things go roughly according to canon-except maybe I don’t know Jaimie and Cersei are definitely Aerys. Or at least there is substantial doubt-as Aerys and Joanna in this timeline remained on good terms and Joanna remained in King’s Landing. Same with Tyrion.
Jaimie and Cersei have very very light blonde hair and bright eyes-green eyes, but Targ seed is relatively weak. Tyrion the same.
Tywin mostly can’t retaliate because he has no definitive proof of his wife’s infidelity, and Joanna fervently claims they are his. She dies when Tyrion is five of the pox. And Cersei doesn’t ever visit Maggy.
Tywin in this timeline is far more reticent in his ambitions-he has the nagging feeling that perhaps none of his children are his, or worse only Tyrion is. He can’t prove it. And even if Joanna was cheating on him-that doesn’t prove for sure who the father is. As she wasn’t not having sex with him. Being a pride obsessed man-this eats away at him and he can’t help but look at his children and see Aerys.
So Tywin is basically cold to all his children, and basically is waiting for an opportunity to disinherit them all.
The opportunity comes when about a year before the rebellion-he catches Jaimie and cersei doing the twincest. On top of that Aerys snidely remarks how Joanna cried out his name during the Tourney of Harrenhal. With Aerys there is no way to no if he’s just needling the old lion or telling the truth.
Furious-he disowns all his children then and there. And plans to remarry. He doesn’t kill them because of bad PR-and because as said there is doubt.
He basically frog marches all three of them to the docks of Lannisport and sends them away on a ship with a ferocious roar of a warning-return to Westeros and he would butcher them all.
Being teenagers and without any support-the Lannister children end up in Braavos-and manage to acquire a small cottage.
Rebellion happens-but Aerys is captured, and is executed. With Robert as king.
Robert marries Delena Florent, and twenty years later.
Varys is getting ready for his targ restoration plot-and the three lion dragons-who have managed to carve out a fairly wealthy outfit for themselves, somehow. A company that does work in sailing, cartography, and so on-with it’s own sellswords led by a Jaimie Waters. Discreetly approached-an offer is made for Cersei to marry her half nephew-and restore the Targaryen dynasty. She accepts. Also Tyrion is promised the rock, and Jaimie is promised recognition as Aerys son. Or rather they all are.
A war is ongoing in Westeros-with LF having manipulated Renly into rebelling and provoking a coup-leading to a free for all, with Robert’s children being butchered and Stannis slain by Loras Tyrell in single combat before Renly himself was cut down in the battle of King’s Landing by Ser Richard Horpe.
This Baratheon bloodletting leads to a score of old grudges erupting and the realm on the verge of full scale disintegration.
The Dornish are however furious the spider has given Elia’s son to the bastard daughter of the “mad king and the lioness whore” and thus ensuring Tywin’s legacy-false or true is coming for the Iron Throne. Leading for them to marry Viserys to Arianne(that goes some differently no Dothraki sea and golden crown) with Quentyn marrying Daenerys.
Leading the second dance of the dragons-or the war of the bastards of lion and dragon and the scions of Nymeros-Martell.
And who assists the Lannitargs across the narrow sea? Why Aemon Waters of course, who has his own private fleet and empire in the stepstones, their potential sibling.
TLDR: Basically Jaimie, Cersei and Tyrion all on the same “team” and involved in a targ restoration plot against Daenerys and Viserys and the crumbling STAB alliance.
@CarlManvers2019 thoughts? Not my most well thought out idea but it came to mind and I had to write it down.