Attachment seems to only address the effect of a child's relationship with his or her parent. I think a child's development could also be strongly effected by other family members like siblings. The bond between siblings would create an interesting dynamic that could change a child's personality depending on the circumstances. For example, siblings that get along well would make each other more playful and give each other an additional sense of emotional security.
This is a very good point, and I know that my relationship with my sister probably helped shape my personality as I was growing up. I think that this is not often discussed, though, because there are more cases where a child does not have any siblings than where a child has no parent/guardian figure.
I agree with you in that other family members can influence a child's life to a great extent. Being an only child, I think having a sibling might have provided me the opportunity to become more playful and "skilled" at approaching new people around my age. Sometimes I think I'm better with approaching adults than I am at befriending those of my age because as a child I only had interactions with my parents and such.