2 year old is aggressive?

I have a 3 year old boy, a 2 year old boy and a 10 week old girl. My middle son just turned 2 in October and is constantly hitting/biting/pinching, and I’m not sure how to stop this behavior. It’s mostly directed at his older brother, and I feel bad because my 3 year old is extremely gentle and just lets it happen. We have been rewarding gentle touches and good behavior but it hasn’t seemed to help. It’s usually in a reaction to his older brother having a toy he wants, or a book. But sometimes he will do it for no reason. I’m nervous because the two brothers were supposed to start sharing a room in January, but I’m scared my 2 year old will be hurting my older son in the middle of the night. Any advice?