Take a look at this Scientific American Interview with Judith Rich Harris (author of The Nurture Assumption and No Two Alike). The central question of the interview is 'Do Parents Matter?' According to Harris's theory parents matter because of their genetic contribution to their children, which affects personality and physicality, and because of their role in nurturing specific behaviour patterns at home. But parents do not matter much for behaviour outside the home and thus for their behaviour at school, in the workplace and in social environments. For these environs it seems teachers and peers are more important than parents.  

This begs the question whether a parent can be 'better' by manipulating the external environment.  I would like to know whether proactive and interventionist parents affect the outcomes of their children by affecting the schools, playgroups and extracurricular activities with which their children are involved.  If, when I become a parent, the evidence indicates that the 'control' I have over the relative success of my child is affected greatly by peer effects, then I will probably be stricter and more interventionist about those peers and about my child's teacher.  So I will probably be one of those slightly neurotic parents championing my child's move from a worse teacher to a better teacher. I apologise to all school administrators in advance.

Research in economics on peer effects and neighbourhood effects reinforces Harris's conclusions.  I would recommend Stephen Durlauf on this topic, see this book chapter online where he discusses neighbourhood effects and 'classroom' effects as an example of neighbourhood effects.  Skip the technical stuff, it's not worthwhile for a non-economist, but some of the examples in the latter half of the paper are interesting for the layperson.

P.S. I apologise for the 'mater' matter play, I couldn't help myself.