Home Run or Out?

Sorry, son and wife are correct. If he catches it and holds on then it's an out. If he drops it then HR.

Looks like I'm buying dinner. Thanks for the quick response!

Not that this is likely, but could someone hop a fence and catch it for an Out?

Hold on, don't spend the money yet, there is a caveot so you may be able to get off:

6.05
A batter is out when --
(a) His fair or foul fly ball (other than a foul tip) is legally caught by a fielder;
Rule 6.05(a) Comment: A fielder may reach into, but not step into, a dugout to make a catch, and if he holds the ball, the catch shall be allowed. A fielder, in order to make a catch on a foul ball nearing a dugout or other out-of-play area (such as the stands), must have one or both feet on or over the playing surface (including the lip of the dugout) and neither foot on the ground inside the dugout or in any other out-of-play area. Ball is in play, unless the fielder, after making a legal catch, falls into a dugout or other out-of-play area, in which case the ball is dead. Status of runners shall be as described in Rule 7.04

obrady,
Good point, but even when he falls into the dead ball area (the stands)it is still a catch. Had there been less than 2 outs everyone would get a base from the time of the pitch (OBR ruling). I was at this game and had to explain this to a few people in the bleachers.