J.S.
I think 3 is one of the hardest ages... My youngest son turns 4 soon... and I'm counting down the days! I think 3s are harder than 2s since they have stronger opinions AND the dexterity to try to get their way. My 3 year old can be the sweetest kid in the world one minute and totally antagonistic to his brother the next. 3 year olds also know how to be subtle in their attacks, making the child who responds seem like the problem.
With that said, I suggest having your son pick his favorite 1-2 toys that he doesn't want to share for any reason and have those put away when your nephew is there. Or have toys that are sharing toys -- for both of them to use -- that are separate from your son's toys, and the only time they get used are when your nephew is there. Both of the boys are at "mine" ages, and your son has the advantage of being on his own turf. If you've just started, give it time, at least 2-3 weeks. Adjustment is hard and both boys are learning the new rules and boundaries, both with stuff and with your attention. The rule at my house has been that if a toys is fought over, it goes away... OR they (or you) can decide who gets it first and set a timer for 10 minutes. When the timer goes off, the other child gets to play with it for 10 minutes. Make sure they no that NO ONE gets to play with it if they fight over it, and they'll figure that out quickly.