Gavinmad
Mr. Poopybutthole
No, he really isn't. Tyrion is Tywin's true son, which is probably part of why Tywin hated him so much. Jaime is absolutely on at least a partial redemption arc, because once upon a time he was clearly just a villain, and now he's someone you can actually sympathize with.
And he didn't do a thing to take that Castle aside from threaten Edmure. Now maybe he would have done everything he said, maybe he wouldn't, but threatening to do it is not the same as doing it. And Tywin damn sure wouldn't have given away a Valyrian steel sword, twice. I'm guessing that Jaime returns to the Kingsguard and Tyrion becomes the head of House Lannister, if they both survive.
And he didn't do a thing to take that Castle aside from threaten Edmure. Now maybe he would have done everything he said, maybe he wouldn't, but threatening to do it is not the same as doing it. And Tywin damn sure wouldn't have given away a Valyrian steel sword, twice. I'm guessing that Jaime returns to the Kingsguard and Tyrion becomes the head of House Lannister, if they both survive.