We have the same problem, my two boys fight over everything...I mean EVERYTHING...really trivial things. It's hard not to punish the older child who "should know better", regardless of who starts it. My boys are a bit older though, 6 and 3 years.

What I generally do, for example, is if both of them are behaving unacceptably (ie fighting over turning pages), then I'd stop the activity and tell them you won't be doing the activity (ie reading the story) with them now because they are not behaving. Maybe send them to their room for time-out for 5 minutes and tell them when they come out that if they can behave then you'll finish reading the book to them.