Thanks all.
Constable Bertrand: I use Aleene's Tacky glue for most of the basic construction. It's a thicker, less wet version of PVA that sets up fairly quickly, I also find that it doesn't seem to induce warping very much but then I spread it thinly and evenly.
I also use superglue, the runny kind, mostly along any edges where cardboard is likely to suffer abuse. I spread it along with a piece of scrap cardboard and it soaks into the cardboard and hardens it. Then you can sand it with very very fine sandpaper.
Now for pictures of kid proofing (sort of) paper shipping containers.
Here are some cardstock shipping containers I built, these ones from Tommygun, although his download site seems to have disappeared.
http://www.warseer.com/forums/showthread.php?226343-Tommygun-does-what-with-paper/page14Other good (and free) sources of paper containers include Antenociti
http://www.antenocitisworkshop.com/news/free-papercard-craft-containers/ Toposolitario
http://www.toposolitario.com/workshop/index_papermodels.htmlHere you can see modifications to make it into a Firefly BlueSun container. Done using GIMP.

Make sure to colour the edges. It's easier done now before assembly. Printed on 110lb cover stock.

Lightly score the fold lines with a dull blade or pen. Makes all the difference when folding to get straight edges.

Cut out and fit in panels from whatever foamboard/cardboard/illustration board scrap cutoffs are about.

Using Aleene's Tacky glue spread thinly to glue the panels.

Assembling piece by piece and folding as I go. A bit of a puzzle to make sure can assemble properly while adding reinforcement pieces.

At this point I hot glued several pieces of gravel to give weight to the piece. Keeps it from sliding around on the table.

Last panel to be added is kind of tricky so I reinforced with some cereal card and foamboard instead such that the panel can close properly.

Here is a selection of completed containers.

I pretty much do this to all cardmodels using various materials. More photos to come.