Let me start off with a fairly important note and that being that I have no serious 4-wheel overland experience.

My experience is driving across Europe in a van (all paved roads so no great challenge) and getting the same van stuck in sand on a remoted Estonian forest trail!

But I have looked at 4 wheels as the way to go for trips now as I have two kids and while my girlfriend likes bikes, she prefers only shorter trips. And I have ridden in South America.

My van is a FWD 2.0TD Transit from 2000!

It is L1H1, so about the smallest proper van size you can get. I bought it as a trip van and workhorse for carting myself and the kids (and dogs up until recently) around the country.

For the latter, I moved the rear seats back so the the rear area is now smaller and the passenger leg space larger. I also build a "folding" bed of sorts that I can open out and lay over the rear seats once they've been folded down. There is also a small fold out table. That is the extent of my creativity at present.

I'd like something bigger so I have also looked at the likes of the Merc Sprinter and VW Crafter. They are indeed big.

They are also expensive.

The reality is I can't stretch to one of those, at least not right now. This forces me to make some considerations.

So finally the part that relates to you:

If someone magicked up flights to Argentina for my kids, girlfriend, van and myself, I would feel confident in doing 95% of the things and reaching 95% of the destinations I did two-up on my R1150GS 14 years ago. This is partly because I suck at off-road riding on a heavy bike and a van like that with decent tyres is not entirely useless. It is limiting to a point but not useless.

OK, with that out of the way, the next bit is to say that my van is smaller than I'd like but, as I explained, I can't afford something 17 times more expensive. My solution?

A roof tent. As yet not bought but it's going to be an Autohome Columbus or Maggiolina. In my case, the large, but for your kids' ages, the medium would also work.

So you can get a smaller van and fit one of those and still have all your spatial needs addressed.

I say van, rather than Land Cruiser or pick up, as I personally enjoy the space of the the former.

So if we entertain both smaller and longer van chassis but agree that 4WD is preferrable, then have a look at the 4x4 Sprinter, the VW Transporter 4Motion or Syncro, the Toyota Hiace and I think there is a 4WD Iveco out there too. (The Daily?)

Note that certainly the Syncro VWs have a viscous coupling as a means of engaging AWD; the same system as some Subarus, IINM.

I won't bore you with my understanding of how it works but suffice to say that if not treated correctly (eg towing a Syncro by lifting the front wheels into a cradle and letting the rears stay on the road) then the VC will be toast and they are not cheap. So be sure to check that out. How is a question for the gods of Google.

Finally, you know when an elastic band is old and snaps at the first exertion? Well, that sums up my lower back. In other words, if there is one thing I would change about my Transit, it would be head room. There's a lot to be said for being able to stand upright in your van. At 2m tall one of you will really appreciate that, even when sitting down!

So a decent example of a reasonably sized H2 van with 4WD capability: €15-20K?
A decent hard-cased roof tent: €3000
A roof rack (mine is from Rhino Racks): €200
Some customising of the inside for seating, cooking and storage: €2-3K? (if you get decent stuff. <€1000 if you build yourself and use timber)

Reasonable budget: €20-25K.

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Adventure: it's an experience, not a style!
(so ride what you like, but ride it somewhere new!)