Family of four in a serious off road trailer is a hard hit to be honest.
I would take a look at some of the AFrame trailers, by Chalet, Aliner and Rockwood. They have what they call off road versions, not serious, but fire road worthy I think. I drug one around for about 8 years or so and never had any problems. Never did a real trail, but it managed to get me home every time and my road to my house is rougher than most fire roads.
The small AFrames sleep at least four and semi comfortably. Are light enough for most jeeps and FJ's to pull with no problems. They are quick to set up, and offer little wind resistance. Not the quality of the ones you have mentioned, but your first qualifier took their requirement out.
I loved that I could be in mine all set up in 30 seconds. Snug, warm and no wind or rain. Stand inside to cook, or on the outside BBQ. I had the larger ones, but the new mini ones offer a good base camp set up. If I were looking for what you have described, they would be at the top of my list.