Thank you for the great advice,
masiman! Yes, that is a WeeRide. My first choice would have been an iBert, but the WeeRide was sitting in my friend's garage unused... so the price was right! All in all, my train cost me an additional $60 (for the used Trek trail-a-bike). I do have to cheat my legs out slightly, but not enough to cause difficulty. The ride is really pretty good!
I will definitely upgrade the brakes. I've got 300 lbs worth of people I'm moving, plus all the gear. When we go downhill, I need the brakes to uh... break!
Now, doing narrower, smoother tires, would that effect balance? I do feel like balance is the thing that I'm most concerned about. I'm usually quite fine pulling everything. It's really not that bad at all! When my 5-year-old is riding the trail-a-bike, her balance isn't very good & it can start to throw me off.
I'm looking forward to more nice weather & longer rides! So far... it's been really great!