Do any kid size (205 mm or 32 EU) ski touring boots and bindings exist? The smallest size I'm able to find is 220 mm, 35 EU.
Here is the link with more description: https://www.camp-usa.com/product/brands/contour-skins/contour-startup-ski-touring-adapter/
And here is a video on youtube how the adapter works: https://www.youtube.com/watch?v=P8Exg3U56ZQ
the adapter is heavy as is the entire setup (downhilll skis+bindings+adapter+boots), if you want to take your kids out to backcountry for more than 30-60 minutes, this will be very heavy for them... Instead, take an old pair of downhill skis, rivet the climbing skins to them... attach cross-country binding and put them in cross-country ski boots. Put the downhill skis + boots in your backpack....