A Toyhauler bumper pull using a van as your tow vehicle sounds like the best trailer solution. The toyhauler garage area can be built to meet your needs...bunk beds, separate rooms...etc.
A 5th wheel limits passenger comfort while towing. You would need a crew cab pickup which can get tight for 6 people during long drives. Although the 5th wheel gives you the best floorplan options. I've seen several with bunk beds and 1/2 baths for the kids.
Rather than a Class C, I would go for a Class A with bunk beds...maybe an ex-tour bus would work.