I've also been trying to find a trailer that is stout enough to handle backroad washboard and dirt roads in the western US. I've been down some BLM roads in far SE Oregon in my older F250 & FWC Shell that I'd love to explore with a small trailer but 20 - 40 miles of washboard is daunting for what I see out there.
Most of what is out there does not seem up to the task. Given that you are trying to accommodate a family of 4, Outdoor RV's lineup is the only one I've seen that might fit the bill. At least that's the case they try to make in their marketing. I have seen a fair amount of them here in Oregon. They are based in LaGrande, OR. They tout their heavier duty frame and suspension system. While that may be true, my bigger concern is how they secure all the cabinets and accessories crammed inside to insure they don't bust or tear loose, etc. So many conventional trailer companies market "backroad" models and cite their raised suspension and knobby tires without changing anything on the inside. I've read a few threads from people on Expedition Portal on the same quest and read some horror stories. I was considering taking a closer look at Outdoor RV's smaller 18 ft unit (that's 18 ft floor length). Dry weight is 5,200 lb and total length is 23.2". Again, that is their smallest rig. They also stopped making units without slide outs. That and their height killed it for me as they would not fit under my car port.
I've heard good things about the fiberglass trailers holding up better than the stick built ones. Many folks swear by Casita's. As for Escape Trailers, they look like a step up from the Casita. However, they are advertised as 2+ season and a family of 4 might be tight. I recall they have stuff hanging off the bottom as well. From what I've read and also based on input from a friend who bought one of their 19ft units, the Oliver Trailers out of Tennessee are the top of the line Fiberglass units. Double wall fiberglass shells, 4 season, fully enclosed bottoms, and the cabinetry is molded into the shell so it can't tear out. My friend has had his for 2 years and taken it down some long stretches of what he called "old growth" washboard and it came out fine. Having said that, the largest one is 23.5 ft. I've been inside one and it would be a no go for a family of 4. 7 feet wide on the inside. Also, expensive starting at 45K for the smaller one at 53K for the 23.5 unit. I've also heard that the Canadian BigFoot brand is stout and 4 season.
I currently have a 1971 23.5' Airstream and, while I've had it down some gravel roads with washboard in eastern Oregon over the years, I don't like to do it for any great distance, as it rattles the hell out of it. So far, it's standing up pretty well but I prefer to keep it on or close to pavement. While back in the day Airstream made great press when dragging them around the globe on Caravans, those trailers were lighter and not loaded with all the amenities available today. Those trips also took their toll on the trailers. Given the cost and added weight of todays Airstream, I wouldn't buy one with the intent to go off pavement. Having said that, I know people do it.
So, from what I've seen today, there is nothing currently available in the US that is up to the task. Unfortunately, the Australians seem to have dialed it in with serious backroad trailers to choose from. I believe some attempts have been made to market in the US but I don't believe they've taken hold. One brand, (Black Series I believe) currently being sold out of LA is actually a Chinese knockoff of an Australian trailer. There is a thread on it on Exp Portal Forums.
I recently came across a smaller, cargo style trailer based backroad camper called Trail Marker Outdoors out of New York. However, not really suitable for a large family. While they have several models, I believe they are all custom made to order. Basically, they can be used as a toy haulers for a motorbike or 2 or a small quad and offer sleeping, cabinetry, solar, power, awning, outdoor showers and can be upfitted for cooking or running water. No internal showers or toilets, other than a porta potty option. They have all aluminum frames & floors with honeycomb walls. I believe the company actually doing the building has a long history doing commercial command center type trailers for the government and law enforcement. They look pretty stout and I think they could handle the backroads well. Of course, they are not intended for hardcore 4x4 overlanding. I'm exploring getting one of these units to replace my 20 year old F250 and FWC Shell combo. Basically, the trailer would fall between what I currently have going with my shell and a fully outfitted FWC. However, it has the advantage of my being able to tow it down some of the many NFS or BLM roads and unhooking it as a base camp set up for a few days while my wife and I explore the area. The one downside of a truck / camper set up is if you want to go out and explore an area for the day you have to break it down and stow away whatever you pull out the previous night. Of course, that speaks to the issue of tradeoffs, which are always there. Too bad the Trail Marker outfit is 3,000 miles away. They will ship, but that adds to cost. Not sure what I'm going to do at this point.