The best answer as previously stated is option C - van and trailer. A few notes:
* No need to buy a new vehicle if will be used mainly for camping. It doesn't sound like money is a huge concern but a $20-$30k used diesel vehicle should have excellent performance and reliability.
* There absolutely is no perfect solution in some cases. This has been hard for me in my RV pursuits. I've been from popups to toy hauler, to travel trailer, to Trailmanor to motorhome (Class C). Unfortunately there is no configuration to date which has totally satisfied me. However, if I were in exactly your situation, the van and trailer would be an excellent "least squares" fit.
* Van - an extended passenger van would allow the youngsters to spread out and invite friends. More room for the family dog if you have one. Additional storage can be had on the roof or in the TT. The van is also great or family trips without a TT. A large SUV can also do this but not as well as a van.
* TTs will have more configurations with bunkhouses - which is exactly what you need. Don't underestimate the benefit of having full time beds. In fact, I would value full time beds higher than the benefit of motorhome convenience compared to the need to hitch/unhitch, etc.
Try to test a number of units out and rent a motorhome before you buy - if only for a weekend. Then you'll have a much better view of your wants/needs.
