I'm still entertaining the possibility that it did not fail. Jamie is yet to act and clearly has a future in the plot development, as does Breanne. Something about Breanne tells me she is the one of the few who might overlook his history of incest and betrayal...
Well, Caitlyn was thinking "trade Jaime for my two daughters." so that's what I'm referring to, I guess.
But Jaime himself has stopped being just 'someone to exchange" and actually someone acting under his own volition. Even with caitlyn gone, he has taken active part in protecting the stark girls to what little degree he could. This is not the Jaime that was in that cage back in Robb's camp, with the false bravado and killing his own cousin to escape. His journey with Brienne and his maiming changed him, made him a vulnerable human being again, and Brienne brought out the best in him. She realized he was more than just "Kingslayer" when he finally shared with her what he did for the city (why he killed the mad King) and started treating Jaime as the man he could become (the man who was willing to bear years of shame in order to save a city of people), not the man he had been acting like or the man he was with Cersei.
The guy who sent someone flying "in the name of love" in S1E1 is not the same man that exists today.
I am not sure if Caitlyn was aware of all that, but she did ask a son of the family who murdered her husband to have her daughters released (a risky request)... and now he has found enough honor to protect them as best he can.
@Cherry: Isn't it clear? My guess is that Tyrion is going to pick Jaime. I didn't read the book, but it's the one way he can dick over his father's plan. If a member of the royal family does trial by combat, a King's Guard has to defend him. That would be Jaime.
Jaime had promised to quit the Guard when Tyrion pleaded guilty and got sentenced to the Wall, but Tyrion didn't do that; instead, Tyrion changed the plan. If Tyrion asks Jaime to champion him, he will; they are brothers, Jaime told Tyrion he could trust him, and he knows Tyrion wanted him as champion way back in the Vale. They are both also spiritual kin: Both saved King's Landing in their time, and both have suffered nothing but abuse from the people of King's Landing for their heroic sacrifices. It binds them. They are the most virtuous in the remaining Lannister clan.
Tywin is screwed. If Jamie champions Tyrion, either they both live or both die. If both die, Tywin gets no heir to House Lannister and the family name dies. If both live, Jaime is no longer obligated to quit the Guard, and Tyrion is free to do as he pleases and Tywin has to suffer the political fallout. The only heir he'll get is if he makes Tyrion to be the new Lord Lannister. In fact, it's in his best interest to send Tyrion away from King's Landing ASAP. Tywin has been completely blindsided. It's quite lovely.
Tyrion basically said, "fuck family" by going for broke; the only family he has anymore is Jaime. And I think Jaime's fed up with dad and sis as well.