As a former 3rd gen 4runner owner, I'll echo what others have said. The 4runner is too small for 4 people + gear + trying to sleep in the vehicle.
You mentioned having 2 people in a RTT and 2 people in the vehicle. So...where does all your "stuff" go? Because the only way to sleep 2 people in the back of a 4runner is to put all the cargo somewhere else. Outside? Also I would point out that neither the 3rd nor the 4th gen 4runners have a flat load deck when the seat is folded down. The seat back slopes up at about 15 degrees which means you either need to figure a way to sleep with that or construct some kind of platform (which would likely preclude you from using the back seats.)
My two 4runners (a '99 3rd gen and an '07 4th gen) were adequate - but barely - for one person and all my gear. When I slept I was able to stack all my gear to one side of the sleeping platform and sleep on the other side. But it would have been impossible to do with 2 people let alone 4.
The 3rd gen also has an Achilles heel in the form of a tiny 18.5 gallon fuel tank. Assuming you get the 3.4 with the slush box, don't count on getting more than about 18 MPG and that's under ideal conditions. With a margin for safety you're talking about needing fuel every ~250 miles/400km or so.
Don't get me wrong, I'm not trying to knock the 3rd gen I'm just saying it's a great vehicle - for a single person or a young couple. On mine I carried extra fuel in RotoPax cans on the roof.
If you want to travel long distances into the back country with 4 people you might want to consider something like a Tahoe/Expedition/Sequoia or even a crew cab truck. As for the sleeping arrangements, if you have to sleep 4 people in the vehicle I think a van of some kind is the only realistic option.
A full size crew- or extended cab truck with a 6.5' bed and a topper with a rack for an RTT could give you the space you want. It won't be as "capable" as the 4runner but it will probably keep your family a lot happier. A Suburban would also work. Unlike the Toyota, GM was smart enough to make the Suburban with a flat load deck when the seats are down. 8' long and 4' wide: