Could you build some contraption that would allow you to suspend the kayak in midair? I'm picturing a large wooden frame with two big nylon straps hanging down--one for bow and one for stern. You could then have a small stepladder for the kids to use to get into the boat. Probably labor-intensive and materials-intensive, but at least they could sway side to side in the boat.

OR you might be able to do it with four heavy sawhorses and some long rubber bungees with the metal hooks on the ends (available at Home Depot--I use them to lash my yak to the car roof). You could wrap one bungee around the end of the bow and another round the end of the stern--then attach each of the four hooked ends to the sawhorse on that side. That way the boat is kept upright but will still shift around. If you can't find bungees long enough, you could hook two of them together and put foam under the hooks if they rub against the boat.

I grew up near Ft. Worth, btw.