Other variables: Socio-economic class and number of kids (environment factors) may influence IV because if parents have less money, they may spend more time working than with their kids or if the parents have a lot of kids, their attention will be divided and the time spend with each individual kid will be reduced. Social environment combined with innate traits can influence the DV. For example, even if two kids have a secure attachment style, if one kid is attractive, he may have a lot of social experience because other kids will want to be around him. However, if the other kid is cursed by genetics and is really ugly, he may develop poorer social skills because kids will avoid him. Also, critical events and experiences later in life may also change a persons well being.
I agree that both socio-economic class and number of kids could influence attachment style and well being later in life, but I also think that the having a bigger family could lead to better sense of attachment as the child would have other people to play with besides the mother so he or she would not always rely on the mother to support him or her.