rogue 5 year old

as the total says, I have a rogue 5 year old son, he acts like he is 15 and can do what he wants, constantly told not to muck about, run shout you name it, I also have a 9month old and I feel that my oldest is almost trying deliberately to hurt his brother, I caught him tonight shaking him, other times i have seen him trying to shove my youngest out the way because he is too close or playing with my eldests toys. He is also in a split home as I'm not with his dad, in my house there is me my partner and my boys, at his dad's there is his dad's fiance and her kids as well as her bro g pregnant, my eldest has only really started acting up since we fo8nd out about his dad's partner and he even acts out at school, though I think I know the culprit at school, (another child) we have tried tough love, no shouting, trying yo explain why we are unhappy with what he has done but nothing is working and there is no communication between me and his dad (we had a volatile relationship). What have others done in this situation or similar?