SPOILERS POSSIBLE
I think that by the time Dany comes to King's Landing she will have been told a lot more of the TRUTH about members of her family, especially some of the old king's deeds, that she will be well aware that SOMEONE had to put an end to her father...
As for Jaime himself, I don't think he's repenting in the real sense of remorse over some of his actions - he still feels he was right in killing Aerys, and he knows there is no way he can give Bran his legs back, or restore Ned to his family...but I think he sees that his actions, or at least some of them, came for the wrong reasons...