All fullsize Broncos are 4 wheel drive. Bronco II's came in 2wd and 4wd. If it's 4wd it will have either a transfer case shifter inside it or a 4wd button on the dash somewhere.
You DO NOT need a 'more expensive trailer' and you DO NOT need to take all four wheels off the ground. When a 4wd is in 2wd (4wd not engaged) it is just like a '2wd'.
Go back to that towing place, grab a pair of pliers and pull that guy's teeth out and force him to eat them. Then leave, never to return.