In Europe, they do RV conversions and slide-in packages on SUVs of various sizes, minivans, and MPVs in sizes that are called compact and subcompact here. Think a conversion on a Nissan Versa or Honda Fit, to get the picture. What you have is a camping support package, not a house on wheels.
There are firms in this country that do conversions on minivans, and on smaller commercial vehicles like the Ford Transit Connect and Nissan NV 200 (Fiat-Chrysler America has something coming).
What they do for these, you could probably do for a SUV. Comparing a van-like vehicle to a SUV, for the same exterior size, you have 20% to 40% less interior volume in most SUVs (MPVs do somewhat better). Most of that difference is in the height from floor to ceiling, so if you are just crawling around in the back, not standing up, who needs headroom? SUV versus van, the roomier van is no bigger, just a different image about who is driving it. I drive my van around, let people figure out who I am; definitely not soccer mom, maybe the guy from the church on an errand?
We used to do the same thing in the 50s and 60s in station wagons, put all the seats down, spread out sleeping bags. It worked. Daytime traveling to night time sleeping transitions were a bit of work, as was hauling out the camping equipment and putting it back in the morning, But it worked. SUV is really just a new name for what we called a station wagon,
Air conditioning? That's an interesting problem. When we were doing this, we did not yet have air conditioning in our cars. We did not have air conditioning in our houses. We opened the windows and did just fine. If you think you need A/C for survival, there are portable units you can set up outside; these are made to serve temporary housing like tents.