Now to the discussion of the dysfunctional bat-family - first and foremost to me at least Batman is already pretty screwed up and dysfunctional as a person, there is nothing that is normal about his psyche so its not too surprising that he and his family has a lot of issues.
He acts like a patriarch of anyone wearing the bat symbol... talk about over controlling and obsessive about those vigilantes that roam Gotham.
He tries to impose his values and morals on those that roam Gotham and try to protect the city not caring really about their views on justice - "do it my way or don't do it in my city" - again this goes directly to his need to control everything around him.
DC unfortunately has made him so paranoid and brilliant that he has contingencies for everything - which in other words makes him overly paranoid... I find it amazing that the heroes didn't shut him down after the OMAC crisis since it was his contingencies that caused it ... but Batman didn't care it seemed - he had to protect everyone from the chance that his friends and allies would go nuts - not a trust worthy bone in his body and he doesn't apologize for it either - is it a wonder that he is ALONE - since he has not way to really interact with another human.
I think the only relatively normal people in the Bat-family is Babs and Dick ( I don't include Batwoman or Huntress as part of the Bat-family)... they have relationships, have friends, try to do normal things, seem human with emotions.
Everyone else seems to be missing a few screws (all the various Robins excluding Dick); and anyone who would allow a child (because that is what Damian is) to wear a costume and do battle with crazed killers and whatever villains roaming the street of Gotham needs to have his head examined and his arrested for child endangerment.
So its not really a big surprise that the bat-family is dysfunctional as the Batman himself is the most dysfunctional of them all.