"Jaime Lannister sends his regards."
What does this line mean? What are the implications, the message it is trying to send? Is it a better line than the changed one in the show?
These are questions I have been asking myself as of late. Initially, I wanted to explain why I liked the show's version better, but as I thought about what the book's version meant, I started to change my mind
To be honest, the reason why I liked the show's version better for so long was because I thought it was more impactful. By saying "The Lannisters send their regards" rather than just Jaime, it made the Lannisters seem like a unified front, a great House that is not to be fucked with and not just a singular great man. It would send the message that it is not the actions of a singular person but something that will set a precedent for the House as a whole when dealing with, ultimately, people getting in their way.
But then I started thinking about why Tywin would have them say Jaime specifically. I came to two major conclusions:
1) Tywin doesn't care that Jaime is a member of the Kingsguard let alone the Lord Commander, he still wants Jaime to inherit Casterly Rock. Cersei is the Queen, just the thing Tywin wanted her to be, thus he wants to keep her right where she is. Tyrion is the heir of Casterly Rock but Tywin would rather bring the Seven Hells upon Westeros than see Tyrion as the Lord of Casterly Rock. He has always seen Jaime as the heir, his heir. When he made his vows, Tywin was pissed as all hell, at Jaime, at Aerys, at everyone. But then Joffrey set the precedent that members Kingsguard don't have to serve for life with the dismissal of Baristan Selmy, thus opening up the path for Tywin to make his wishes come true.
Several time through the series, we see the song "The Rains of Castamere" used as a threat, a reminder to any and all of what Tywin Lannister is capable of. The ruthless destruction of Houses Reyne and Tarbeck solidifies Tywin's fearsome reputation and I believe the Red Wedding is meant to be Jaime's Castamere. By giving him the responsibility, Tywin is securing Jaime's legacy almost. Already Jaime is well-known for being one of the greatest swordsmen alive, but he needs to be more of a threat, more of a foreboding presence at the back of people's minds than just someone who is pretty handy with a sword. If people believe Jaime capable and willing to do something as horrible as the Red Wedding, what else is he willing to do to protect the realm (or just his family)?
However, similar to Castamere, the Red Wedding is a huge, huge, huge political mistake. It is not a show of power, of skill in battle, of cunning or wit. No, it's a demonstration of brutality. It says to everyone else that the Lannisters will do whatever they want in response to slights, minor or otherwise. The Red Wedding especially does this. Sure, you crushed the Northern rebellion and took out a huge threat to your power, congratulations. Now no one trusts you or respects you or will want to be by your side. They may fall in line out of fear, but fear can only hold people for so long and to such lengths. Tywin os still upset, to his dying day, of the perceived failings of his father. He hated how his bannerman laughed at him, hated how a "whore" wore his mother's jewels and clothing, hated the weakness he saw. But I would argue it is better to be underestimated yet respected than feared yet reviled. When the going gets tough, who will come to Lannister aid after this? After this violation of a sacred law, Guest Right, who would ever want to be on the side of Lannister?
2) This is more of a narrative reason, though I certainly believe Tywin may think similarly, but this line is also a twisting of the knife. Cat let Jaime go and everyone and their mother told her what a horrible idea it was. Now, it's come to bite her in the ass. Had she not released Jaime, I am not entirely sure the Red Wedding would have happened but that is a whole different discussion. Fact of the matter is, she did and now she has to watch her son be murdered in front of her. How could she not blame herself? How could she not blame the Lannisters for being cravens wholly lacking honor? How could she not blame the gods for their cruelty? This line is the cherry on top of the tragedy of the Starks.
While (iirc) Tywin did not know Catelyn was the one who let Jaime go, I believe he thinks he somehow escaped on his own, I do think he would also view it in the same way. As consequence of taking his son, and of letting him slip through their fingers, their lives are forfeit. Yes, when they rebelled their lives were forfeit to begin, but I think Jaime's capture pushed Tywin to such a drastic means of dealing with them.
At his core, Tywin is a petty, vindictive person who values getting his revenge more than actually doing what is best for the Lannister name. True, he may believe this is the best course of action, but that just goes to show what an emotionally-driven, lack of forethought moron Tywin truly is. He is not clever, he is cruel. Do not confuse the two. And, much like every other Lannister, Tywin seems to believe because the Targaryens conquered and kept the peace through fire and blood, he can do whatever violent acts he wishes and history will laud him for it, but he is not a Targaryen, it does not work the same way. Targaryens for centuries were viewed as closer to gods than men, Lannisters never were held in that esteem. All he is doing is dragging the Lannister name through the mud.
One of the things that makes Tywin Lannister notorious in Westeros is told about in the song "The Rains of Castamere," which details how Tywin brought about the end of House Reyne and House Tarbeck, serves several times as a reminder and threat of what Tywin Lannister is capable of ie complete ruthless brutality. It is intended to keep people in line and to keep their noses clean. I believe Tywin wanted to give Jaime a similar reputation.