FYI - Lori isn't mad about Rick killing Shane. She's upset that Carl shot him when he was in Zombie mode. As Rick is telling her everything she's not really showing an upset reaction, but when he says "Carl put him down" after telling her that he turned she pretty much freaks out.
She's not a great character but its mostly just because the actress that plays her is fairly terrible. Go back and rewatch that scene and you'll see what I'm talking about, but you'll also see some fairly terrible ing acting from her.