I agree with the people who said that Jaime is disliked by the majority of Westeros for his oathbreaking. The oaths are like the traditional rules of Westeros so its more than just switching sides in a war, it is a deep part of their cultural establishment. Knights of the Kingsguard are fabled, they are remembered in song and story. As we know many other knights in the kingsguard have broken their vows, but what Jaime did went so far beyond, I mean his one job was to protect the King, and instead he killed him. I don't think people like Ned Stark or the majority of Westeros care if killing Aerys was right, they are just going to judge him as an oathbreaker and dislike him for it. Most people don't know the city was going to burn either because Jaime kept that oath of keeping the King's secrets (*sigh* oh Jaime).

I agree with your point about Tywin though, Jaime is probably seen to be a part of that simply by being Tywins son. I think that is what bothers Jaime the most of everything because he did like Rhaegar and I don't think he wanted his family killed like that even if technically it almost had to happen in Roberts eyes because of his Targ hate. I believe Jaime when he said he didn't know they were killing Elia and the children.