Answer:
There really isn't one. Kid's bikes as a rule are intended more as toys than as something to go for miles on. Best option for bike touring with a kid is probably a trailer bike. Otherwise you just have to do your best with what's available. I'd probably start with a BMX, kit it out with a flat bar on a short stem and try to find some shorter cranks for it. That, and a custom rear wheel with an IG hub is probably the best you can do on a limited budget.
It'd still be far from ideal though, the bottom bracket will be unproportionally high and depending on the kid the distance between bar and pedal can still be too long.