Welcome to the board, Mike. I don't have kids yet (and don't plan on starting for another 4-5 years) so I can't help you there. Do you have another car? Perhaps a 4 door?
I'll be honest. As much as I love the 370z, I would say it'd be a bad choice with a 1 year old child and without a second car. Although, right now you can get a cheap second car (for like $1-2K) and have a car to drive your son around until he's old enough to sit in the Z!
The Evo has back seats and that makes it a nice daily even if you have very young kids. I wish you luck in your decision. I'm sure there's lots of guys on this board that are in the same (and very lucky) position, having children.