I finished all the main components of the steering. I just kinda guessed on the lengths of all the lever arms involved. I still need to adjust the tie-rods so the wheel is straight and the turning radius is basically the same in both directions. And I need rubber washers everywhere a bolt head and tie-rod end rub each other. But overall, seems like it should work out fine.
I made some tie-rod ends by welding a nut to the end of an all-thread coupler.
To keep the steering rod centered and smooth rotating I made some inserts for each end out of UHMW
Kid sized Batpod 
Looks good. Perhaps one tip for the steering I learned by experimenting with my Batpod Jr build. As tires are quite wide the steering angle (in the hub) needs to be quite shallow. The shallow angle helps the bike to tilt automatically towards the direction you are turning to. If the angle is too steep the bike has a tendency to stay upright and thus resist turning. I found that about 17 degrees was about right for my build. With that the driving became effortless and easy for kids to handle as well.