I get a sense that the word "compromise" is not part of the vocabulary in this discussion. Unfortunately you will need to learn the definition of the word to find a solution.
Big families are a tiny demographic in the RV industry. You need a vehicle with a massive passenger compartment, a massive cargo capacity, and a massive towing capacity. Unfortunately no such thing exists, so you will have to compromise.
1. Deal with close quarters on the trip. That's a crew cab pickup truck that you will need to compromise on, if you insist that you need that 12,000lb bunkhouse travel trailer or the 40' 5th wheel.
2. Deal with close quarters at the destination. That's the smaller, lighter travel trailer you will need to compromise with a tow vehicle with more passenger space such as a 3-row SUV or even a 1-ton van.
3. Deal with not traveling together. Get the pickup to tow the trailer without regard for passenger capacity, and have one parent bring the trailer, while the other drives the family's daily driver with the kids and dog.
There just doesn't exist a tow vehicle with the capacity for a big family and a big trailer. A 1 ton van is as close as you're going to get these days, but tow capacity is limited to about 10,000lbs, diesel is not an option, and you then get to drive a full size van around all the time.
Someone will inevitably recommend the Ford Excursion. The last one of those was built in 2005, making it 16 years old. Low mileage barn find creampuffs are far and few between.