TurboWithAKick I think it does happen sometimes. One child is the scapegoat, and all the parent/parents negative emotions are projected out and away from the parent/parents as being caused by, or the fault of, that child. The parent/parents are then able to cope a lot better with their other children, and a virtuous circle is established in the parenting of those.
Of course, a vicious circle is established with the scapegoat child: they are already single out as the cause of parental bad-feelings, as a child at fault - on top of this, the constant ill-treatment will have an effect on their behaviour, and in addition, the parent/parents will feel enormous guilt, which will add to their already unbearable internal feelings.
There must be research on this, and also research on which children are most at risk of being the scapegoat child.
But we do get threads on mumsnet asking how to deal with feelings like this. I always feel so sorry for the parents who post - they must feel so out of control - wanting to stop (hence posting) but not able to do so. I hope they get help.
I have no idea about this case, at all. to be banal, I feel very sad about it.
However, I would say to any parent reading this, and feeling overwhelmed by parenting, it is OK to go and see a GP to get help. They are very non-judgmental (in the main), after a few years in practise they have probably come across it before, and will point people towards help.