Internal Gear Hub for 16in Wheel? My 4yr old son has a 16in Bikestar and at times he maxes out the gearing on it trying to keep up with his old man.  How feasible is it to add either a 2 or 3 speed hub to such a bike?  I'm concerned about how much space the hub is going to take up and since I doubt the wheel is a 36h, can one be used with less spokes?  I know kids grow out of bikes quickly but he is going to have this bike for a few years for now, and this wheel could be passed down to his sister (right now I'm planning on getting the same brand).

While cruising the flats it seems like his cadence is getting close to the high side while doing 7~8 mph.  Any bit of downhill causes him to max out and spin crazy.  When he wants to pick up the pace a little will also cause him to spin crazy.  We have a few hills along our favorite routes that he struggles on so I can't just swap out the existing gearing.  The front chain ring fills the chain guard so that is out of the question as well.

BACKGROUND INFO:

Ok, so I was mostly joking about the keeping up part, I let him lead and set the pace.  When he falls behind, I slow down and let him pass, but stubborn kid likes to follow the trailer ...uh princess chariot... too.  He also rides this bike daily to daycare and back (2 miles one way).  

This bike was picked with commuting in mind.  We got him this bike for his 4th birthday and about a few weeks after ditching the training wheels.  He just barely fit it then and rides great with it now so we still have some time with it before he gets a new one.  

Alternatives won't work as well since who wants to downgrade?  He loves having his own bike.  A trailer bike would probably not mesh well, he is already trying to attach his sisters trailer to his bike (and I'm tempted to let him).  Long distance isn't an issue with him either, his first ride without training wheels on a 12 inch bike was 15 miles and his first ride with this bike was 21 miles.  The common "long way" home from daycare is 10 miles itself.
It's pretty easy if you have a spoke cutter and are willing to run a funny spoke pattern. I suggest buying (ideally second hand) a three speed hub and lacing it into the 16" rim yourself. With a wheel that small and a child on it there's not enough load to make strength an issue, so you can reasonably either lace a 20 spoke rim to a 36 spoke hub using whatever holes are closest, or ignore two spoke holes in the rim and use every second hole in the hub (18/36). It's probably not going to be pretty, but it will work.

However I think you're going about this backwards. Why are you riding faster than he can? Much as you wouldn't suggest stilts so he can keep up when you walk, gears don't address the problem that you can ride faster than him. He doesn't have the power or endurance you do, so without a power assist he's going to be slower.

If you need to cover long distances, perhaps a trailer bike would be a better solution? That way he can "help", and you can go whatever speed you like. That's generally safer for your kids, since you're in control and the only real risk is them jumping off the bike while you're moving.