You're making good progress. I like the thriftiness of the build.
You mentioned in an earlier post the waterproofing mix. It is 50% mineral spirits/50% polyurethane. It is great for waterproofing the wood prior to finishing. Give it 3 or 4 coats and let it soak in. More on the edges and ends. Will cause a very slight ambering effect on the wood. I've used it on my wood where it won't otherwise see a finish. According to GPW, who has used it extensively, it works great prior to paint and some other finishes. Don't know that it does a thing for foam...
The hard exterior shell of the foam is usually canvas and paint or another alternative. The heavier weight of the canvas, the stronger the "shell". I guess tree limbs and RV's don't mix too well no matter what you have as a shell. Maybe aluminum is the strongest siding and you can do an aluminum side but the $$$ involved and the added weight are a definite negative. I used fiberglass. Messy, not inexpensive and the cure time is long but I like the nice smooth finish. I thought about a thin 5mm exterior plywood, but don't like the possibility of rot, and the weight is a negative, too. Your choice. If your budget is the biggest issue, I'd go with canvas using thinned out glue or exterior latex paint as the adhesive. If $$$ are no object and you're looking for durability and strength then aluminum could be your answer
Bunks on one side, a hammock for the small one and for you.... a platform/floor and a thin pad sounds like roughing it to me although I gotta admit that the self-inflating pads that they sell for backpackers are really pretty comfortable. One of the reasons I'm building a teardrop is so I can a couple of the comforts of home with me. A soft comfortable place to sleep is one of those. (Beer on tap is another)

Take a look at the camping section of REI, Cabelas's and the like and you can get some pretty nice pads. Should work nicely and those pads are easy to roll up each morning to keep them out of the way. Get a good one though, I've never been successful at patching one of those if they get punctured (normally by some unseen microscopic sharp object). I went cheap at first and after disposing of two leaky but otherwise fine pads, I paid for a good one. Haven't bought another one since. My son uses it now when he's off backpacking or camping.
Hope that helps. Keep up the great work