Steve, looks like a lot of compromises in the making, paddle now, and leave it behind, get something that's ok for now and later? make something to take along? My first response is a yak board by Ocean Kayak (I think) it's plastic, it'll stow somewhat easily, tossable, will fit a grown up but is marginal/doable for a kid (low windage), will make a very user friendly spare swimming platform but you could still paddle a 35lb anchor on it (don't get your toes caught). From there just for the kid is an ocean kayak brand plastic sit on just for kids, bouncy small, and also tossable.
Once you go to a closed deck boat then you open up the possibility of a small boat that weighs 300lbs when flooded. Of course nobody swamps kayaks but it's a concern when the water is cold or you need it on the deck NOW.
For a production plastic kayak a Wilderness systems Piccolo looks like the best paddling boat. A Perception Umiak is the best new deal but the seat has some comfort complaints.
You must have a few pans in the fire, how about getting a spokeshave, a 2x4, an older kid with bandaids to monitor him and have him make a greenland paddle?
look around for a used Piccolo.