Modify geared hub to fit a 110mm frame
I finally got it going using a Shimano Nexus 3 (SG-3C41). Looking at the pics, I figured that I could remove the massive outer distance nuts to make it fit a narrower fork:




This was not quite sufficient to get it to 110mm so I had to make use of an angle grinder to cut a couple of mm off the cone-shaped nut on the right side of the axle.

The most tedious part of it all was finding an 18" bicycle rim with 36 holes. I could not get one, so I ordered a 32-hole rim ending up with three different spoke lengths (3-crossed) in the wheel. It took me some effort to figure out of how to lace the wheel and seems to bring some durability / stability issues due to the difference in spoke tensions, but this is a kid's bike after all so great strain on the rear wheel is not to be expected.