Our son is starting to become a bully (11 y/o)

Hi guys. Our 11 year old son has always had some challenging behavioral issues.For the most part he's a good kid and listens to us and is caring. He loves being the center of attention. He has always resented his younger sister (she is 9 now) and ever since she was born he bullies her day in and day out. There are rarely moments when they are together and things are calm. Like for example just to get a rise out of her he'll hide one of her dolls, or take something that she was playing with, or just give her a push or bad look while walking by. We have 2 more daughters (7 and 5) and he doesn't bug them nearly as much.One of his cousins (a 10 y/o) was complaining that my son was making fun of him for something, and he had tears in his eyes. They used to get along really well so that came as a surprise.When he does something wrong and gets in trouble he'll have an over the top reaction like quietly storming out of the house, throwing something, or hiding. It's difficult to discipline his behavior because if we do something like disconnect his Xbox he will pretend like he doesn't care and doesn't even ask for it.I'm just not sure how to get through to him any more and fear that as he gets older he'll just become increasingly rebellious and stubborn.Any thoughts appreciated. via /r/Parenting http://ift.tt/2mEmjM6