How about this cheap and simple solution ...?
Ask around for a couple of old singlespeed bikes or even keep an eye open for them in skips! I've seen quite nice bikes being chucked away.
Take the transmission (chain, cranks/pedals/chainring and bottom bracket) off the more tatty bike and use that as a balance bike. Decide for yourself whether or not to leave the brakes on that one.
I'd buy a quick release mechanism for the saddle height adjustment on the other bike, so it was very easy to raise or lower the saddle.
There would be no gears to worry about or damage so both bikes would be very rugged. (If you can't find suitable singlespeed bikes, remove the gears from donated multi-geared bikes.)
I'm sure if you asked on the forum, you could easily rustle up a few old bikes which are surplus to requirements. In the past, I've given away bikes better than the ones that you'd need.