I ahd an after thought does your sister argue back with him instead of not feeding into it ,as she could have got into a "power" struggle of wills, best to not yell back and walk away letting him get on with it,go quiet and firm and in charge ,, set bounderies and if he misbehaves tell him NO TV No PC No Games till he is quiet.IFocus on his positive side and praise him when she sees him doing something right.
Definatly get his Dad more involved with him thats probably some of what he is missing,as he says he hates him is a clue.ask your sister to contact him for better visits.Has he been like this since the other siblings wre born as he could have jealousy issues and feel left out,how does he behave at school if it is the same and the Teacher has issues with him maybe a counselor would be rght but if he is okay and good at school the problem is in the home.Has your sister talked to him and asked if he is upset by anything maybe some input would be good on why he is upset.