Once again, I have to disagree with you. Vegeta did love. For example, his father. He really loved and looked up to his father, and Frieza killed him even when he told Vegeta that he would leave his father alone as long as the boy did whatever he said. Frieza wasn't merely someone Vegeta didn't want to trifle with, he hated him with a passion because the bastard took everything from him. He was a five year old little boy, brutal yes,I'll give you that because it was part of his nature, but he loved his father, looked up to him. Frieza killing him is ultimately what led to Vegeta becoming as immersed in darkness as he was. Of course he didn't care about anyone after the death of his father. Why risk the same thing happening again if he allowed himself to care too much? You talk about all the Saiyans as if they were completely heartless, when that isn't true at all. Look at Bardock, if you need proof.
On the subject of Nappa, yes that was brutal and cruel, but the fact is, Nappa probably would have done the same exact thing if put in Vegeta's shoes.
Do you honestly thing someone as prideful as Vegeta would enjoy being ordered around by anyone, especially Frieza? Even if his Saiyan nature calls him into things like brutal killing, he most certainly wouldn't like being sent to do Frieza's bidding. I don't know where you got your logic there.
I agree with you on one point, that Trunk's death was the turning point for him, but, my view on Vegeta's goodness differs slightly. It was always there, and deep down I think he knew it, he just didn't want to acknowledge it. Also, as mentioned by King Havoc, Vegeta was the brains of the outfit, especially when he and Goku teamed up. I hate how everyone gives Goku credit for everything when Vegeta is just as important, and lets face it, a much more interesting character.