What is it you want to experience? Do you want to travel and see the sights? Or do you want to camp and enjoy the outdoors?
If the former, you are going to be limited. As mentioned, no suv will tow a trailer that size. You don't mention a spouse, so using a second vehicle may not be practical, even if you would want to on long road trips. And many RV parks don't allow tents. So you really have to do your research.
An option may be to look at a motorhome. But you need to make sure of seatbelts, etc. You could tow a smaller vehicle behind and with your older kids reaching driving age, they could sometimes drive that car in tandom.
If the latter, then looking at a hybrid or even a tent trailer is a good option. Using a tent or two for the older kids. Most campgrounds will allow an RV and tent on one site as long as you are a single family unit.
You really don't need all the bells and whistles to enjoy RVing. And honestly, privacy with 6 people in an RV doesn't exist regardless. So I would not worry so much about doors and separate spaces and focus more on the weight.