I really think that Gunn's interactions with Cordy in 2x03 (I think that was the episode
) were what integrated him fully into the group. Until then, he was just on Angel's beck and call to help HIM out on sole investigations but when Gunn got to know Cordelia on a personal level and she gained his trust, his real personality came out and he stopped thinking so much about his sister and opened himself to friendships with Cordy, Angel and Wesley.
