The biggest thing I would say is to avoid choosing a trailer based on how rugged it looks, but rather pay attention to the real world limitations that will keep you from going where you want and enjoying your time getting there.
To me, the following are the most important things to consider, in order of importance:
1. Proximity to the manufacturer and a good community of owners to help you with issues, upgrades, etc. For example, I would avoid anything from Australia, South Africa, etc. like the plague. You will always have the risk of having an issue that you can't fix yourself, and with anything offroad you're constantly running the risk of damage from bouncing it around, so being able to take it to the manufacturer for repair is essential. As an example, one of the brands in that article is Kimberley, and one of their models was a pop up thingy that they may still sell here. Well, the pop up part was actuated by cables, and cables break. And in the case of that trailer, when they did it had to be completely disassembled to repair them; and at the time I was looking at them there were owners here in the US who had essentially lost their trailers because fixing them meant shipping them back to Australia.
2. Size. A lot of the trailers in that article are literally too large to be allowed down a lot of national park roads. Think about that for a second. If a ranger is going to stop you at a park entrance because the nice paved road through the park is too twisty, how confident are you going to be taking it down an unknown forest service road? I hope the answer is not very. Maneuverability will by far be your biggest limitation with a trailer. So, imo, anything wider than your truck or longer than 25' or so is automatically disqualified from being called off-road, no matter how tough it looks or what they say in the brochure. And I'd probably prioritize that as width being the biggest clearance concern, then turning radius, then height. Watch those tree limbs.
3. How well does it tow? Just because you have an off-road trailer doesn't mean that 90% of your time isn't going to be spent on the highway. Ask around to owners to make sure that it's a comfortable tow at highway speeds. Lot's of off-road trailers sacrifice stability for a showy suspension setup, or just have inherently bad balance. Also watch out for boxy trailers that may not handle side winds well, nor the wash from semis.
4. Build quality. By that I don't mean rugged materials and such, but rather did they use quality connections for the plumbing, did they tie down the wiring so it doesn't vibrate loose, did they use stainless hardware everywhere, etc. Also, is the structure of the trailer inherently resilient to damage from vibration and generally getting banged around? 9/10 what will ruin your trip isn't getting stuck or anything like that - it's going to be the water leak when you get to camp, the broken furnace, or the fact that your lights don't work. Current owners are good sources for information on quality, as are factory tours if you can get one.
5. Watch out for trailers that don't take advantage of the things that make trailers attractive in the first place. If you have a trailer that takes an hour to set up, forces you to cook outside in the wind, has no bath, has a bunch of canvas fold outs that will inevitably mildew, etc., then what you actually have is a very expensive tent. Conqueror trailers come to mind here.
If you can find a trailer that meets those requirements, then it will take you almost anywhere. And I think that almost is enough, because the final thing to consider when picking out a trailer is that luxury in the middle of nowhere is golden. Remember that if you want to go someplace that your trailer won't, or just want to rough it for a bit, your trailer can be considered a base camp from which you can head out for a night or two of adventure. Having that base camp means warm showers, heat, a nice kitchen, etc. that you can look forward to when you get back; and, more importantly, will make your family more receptive to having the adventure in the first place. So don't think that your trailer has to do everything, go everywhere, etc. Find a balance that works for the way you want to travel. Besides, no trailer will go everywhere.
I started out in the same place you are and we looked at everything from rooftop tents to the Australian things to earth cruisers. We ended up with an Oliver, which most people would not consider an off road trailer, but after 7 years of it I can say with 100% certainty that I'd buy the same thing again. Not once has the trailer been the limit that keeps us from going where we want. But, that's for me and the way we travel. Everyone has different priorities and so spend the time to find what's the right fit for you. Get many, many opinions, and everytime you think you know exactly what you want, spend some time living with it in your head. Don't just think about what an ideal trip would be like with it. More important is what it's like when things are decidedly not ideal.
