Ok. I get it - you need more room.
And you want easy access to your gear; not having to climb up and unstrap stuff from your roof every time you need something.
You also don't want a RTT with those little kids. You don't want them falling out, getting them in-and-out of a RTT would be a major pain, and you need room for them to play/move around (especially if it is raining and you're stuck inside the tent). You need a ground tent probably bigger than you think you do. You need room inside the tent for a small kid's potty. In the tent, I recommend cots for the adults so you can store luggage and such under the cots.
You also need a small trailer.
Check out my build thread:
Mini Harbor Freight (type) Trailer Ultimate Build-Up Thread | Jeep Enthusiast Forums (jeepforum.com)
The above is a long thread, but if you can read through the whole thing, you'll have all the info you need to build a very capable off-road trailer based off a HF-type trailer frame. For your situation, if you took a HF-type 4'x8' trailer frame, shortened it to 4'x6' and built from there, that would meet your needs well. Tubs can be built out of lumber, plywood, fiberglass, aluminum diamond plate (which is what I did), or steel (heavy in my opinion). Suspension is a simple leaf spring set-up with a solid axle.
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Mine is based off a small Harbor Freight type 4' trailer frame. It is definitely "Off-road capable and reasonably small". It is quite modified (frame reinforced, suspension & axle swapped out, tongue extended, etc.) but these modifications are easy to do. And it can be built for way cheaper than buying one would cost. Google "small overlanding utility trailer" or variations of that to see what all it out there. They can get expensive quickly.
The old WWII military trailers had a tub that measured essentially 40" x 72" (measured at the base of the tub). Mine pictured above is 40" x 50". It is tall enough that I can stack two 8-gallon Rubber Maid Action Packers on top of each other, and still have a little bit of room on top when the lid closes. And that's the secret - make it tall(er) and with a lid. It is all about cubic feet (length x width
x height) for storage. Mine is about 28" tall.
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I overland with a Jeep TJ (if you haven't figured that out by now). Sometimes there are two of us (two big grown men). There's just not that much room for gear inside a TJ even with the rear seat removed. I have a roof rack on my TJ, but putting lot of weight on the roof can make it top heavy, Mine's pretty light - all I've got up there are four X-Bulls, a 32" light bar, a shovel, winch extension cable... and that's about it. When carrying a kayak up there, I've got the X-bulls on the lid of the trailer. The trailer has been the ticket for me. It is amazing how much stuff you can put in/on a little trailer. Mine has literally tens of thousands of miles on it, much of it off-road. It has made trips into Canda, crisscrossed the country a couple of times, etc. It has and can take a beating. It follows behind the Jeep like a puppy dog. I've also got electric brakes on the trailer and that is helpful (especially for safety reasons). My Jeep's tires are 285/75/16" (33" tall), and the trailer's tires are 235/75/15" (28" tall). The axle is under the springs, and the trailer sits level when connected to the TJ or Willys. The trailer has a spare tire mounted on the back panel of the trailer tub (using a Jeep TJ factory spare tire mount).
And before I put the tent on the top of the trailer, the roof rack you see on the TJ was originally bought and installed on the lid of the trailer for more carrying capability with the trailer (especially before I put the hardtop on the Jeep). A basket on the lid of the trailer comes in handy.
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Check this out:
(217) TJ and trailer - YouTube
I built mine (someone else built the tub, which is really just a big box with a lid). Minimal welding involved (which I farmed out) - mostly it is bolt together. If you can cut angle iron and drill holes (needed for doing the reinforcing of the HF-type trailer frame) you can do this too. I'm a nurse - not a mechanic. If I can do it, you can do it. And what is nice about a small trailer like this is you can keep it 90% packed all the time when not in use, so you can do a quick getaway on short notice if you want.
Plenty of places sell small trailers capable for off-road travel. Main thing is you don't want one wider than the tow vehicle (comparing outside side-to-side tire distance). You can go wider than mine (or the WWII standard trailer) and still be ok. My trailer narrower than my TJ (measured from between the outside of the tires). Behind my flatty the width is essentially the same. Your JKU is wider than my TJ.
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This summer I plan on running the Idaho Back Country Discovery Route. I'm the organizer. And of course, I'll be taking the trailer. It'll be about a three-week 4000-mile trip all totaled. Much of it will be off road.
US Northwest - Idaho BDR (and then some!) | OVERLAND BOUND COMMUNITY
In case you're wondering, that's a Cabela's double sized tent-cot on the lid of the trailer. It functions as my little RTT, and weighs about 50lbs total. I also carry a Browning 8'x10' dome tent (and a cot) in the trailer for if I'm going to be camped in one place for a bit. These next two pictures also show a little better some of the stuff I've got attached to the outside of the trailer (means more room inside the trailer for stuff). I don't have an electric fridge, so I like having ready access to the cooler when adding ice or draining water. Or when I'm cooking on the Jeep's tailgate. Or when I'm stopped and want a quick cold drink out of the cooler.
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And yes, I can still access the contents of the trailer even with the tent opened-up.
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Let me know how I can help you if you want to go this route.
The Pros and Cons of Overlanding With Trailers » Expedition Overland (xoverland.com)
Here's another trailer thread on this expedition portal you might find interesting:
Smittybilt Scout Trailer Reviews? | Expedition Portal
Want to build a WWII type trailer? This'll get you started with a frame/tub/fenders. Finishing it out (suspension, axle, wheels/tires, etc.) would actually be pretty simple, and you could get the exact axle for the trailer that fits your desired wheels & tires for the trailer.
Results for trailers (kaiserwillys.com)
Got a lot of money to spend:
Is an Off-Road Trailer Really Practical for your Overland Adventures? - Bing video (very nice but very expensive trailer, but nice info on the video)
GoFSR Overlander Trailer – Off Road Tents
Rugged 'N Ready 60" High Country Trailer – TO Extreme Off Road (to-extreme.com)
Really, all you need is a large box for storage on a simple frame with leaf springs and a solid axle. After looking at options out there (a few linked above), a HF-frame based trailer starts looking really good.