Tbh im not sure where your getting any of that from and it just seems like stretch your putting to much thought into her words here . Her point was simply that the true "second Tywin" of the family wasn't his "first born" but rather Tyrion. She's worried because at that time, Tyrion was an enemy to house Lannister and was on the loose. Tyrion has it in him to bring them all down and she's worried.
I can find plenty of dialoge with stronger hints pointing to Cersei and Jamie being Targs. If this is supposed to be proof of him being Tywin's seed I'd say it's kinda weak...
You expect these characters to be carbon copies of one another, when they are not. I was just making the point that if you want to look to the past for characters who parallel Jamie, those two would be some of the strongest ones to do so. I don't think the fact that they're both Targs is also something one should overlook.
If you can't see the strong parallels between Jamie and those two men, then I'm not sure if there's any point in arguing over it.
Gennas one of the few people in the world that know Jamie best, as is emphasized in the entire chapter.
Yes Jamie joined for Cersei but I don't think it was ever a hard choice (as he admired the KG) and more importantly is that he chose to stay in white inspite of his father's disaproval. In this way Jamie is definitely like Kevin whom himself is fiercely loyal to House Lannister.
“You were the one who taught me that a good threat is often more telling than a blow. Not that Joffrey hasn’t tempted me sore a few hundred times. If you’re so anxious to whip people, start with him. But Tommen . . . why would I harm Tommen? He’s a good lad, and mine own blood.”
Tyrion killing tommen would have been going overboard. He was just playing the part that Cersei wanted, in order to make her think she was in control.
“Whatever happens to her happens to Tommen as well, and that includes the beatings and rapes.” If she thinks me such a monster, I’ll play the part for her.
In regards to Tywin's thoughts on Tyrion, I'd agree that he suspected Tyrions parantage but I don't feel as if he actually ever got confirmation, as it would have been impossible to test (save for with dragons).
I believe Tywin was aware of the Cersei and Jamie rumors even accepts that it may be true (the guy spent 20 years around targs and he knew Aerys better than anyone ) but Tywin would never admit to it out loud. He's able to accept the possibility that Cersei and Jamie are not his, because they are everything a father could want in Lannister heirs and the realm wouldn't know of his shame.
Tyrion on the other hand is an ugly creature. The walking and talking reminder of everthing bad in his life. Tywin can't even try to pretend Tyrions his and if Tyrion really was born with dragon malformations than it would have been even harder for him to not be reminded of Aerys every time he looked at him.
As I've said before I think the tragedy of their relationship is that Tyrion was truly is seed, dispite his connection to Aerys.
“Dragons,” Moqorro said in the Common Tongue of Westeros. He spoke it very well, with hardly a trace of accent. No doubt that was one reason the high priest Benerro had chosen him to bring the faith of R’hllor to Daenerys Targaryen. “Dragons old and young, true and false, bright and dark. And you. A small man with a big shadow, snarling in the midst of all.”
". . . but every little girl needs a big brother to protect her. Tywin was big even when he was little.” She gave a sigh. “Who will protect us now?” Jaime kissed her cheek. “He left a son.” “Aye, he did. That is what I fear the most, in truth.”"