Even with a larger dolly the fenders can hit the bottom sides of the doors.
I've owned two tow dollies - one 80" and a 85". Pulled a Toyota Sienna with the 85" and had about $1500 in body damage after a tight turn into a gas station in Gardner, MT.
I used a tow dolly for 10 years and they were a pain. Lights would never work, body damange, flat tires, etc. It will keep you out of trouble!
There is usually a grease fitting in the top of the king pin. You may want to try to grease that for the clicking sound. But I think that the click might be the car pushing on the tow dolly fender.
You may want to borrow a smaller van. My in-laws had a Dodge Caravan that was much thinner and would go on the tow dolly fine.
Tom and Katharine
'07 Winnebago Tour 40TD, 400hp Cummins
RVing for 19 years & 150,000+ miles