In all my miles of towing a dolly, I have never had any such incident as described above! In fact, I have only had one trailer that whipped back and forth as described above. It was home-made, and very poorly built.
My Demco Kar Kaddy KK260 is rock solid behind the motor home, with the PT Cruiser on it. Come to think of it, it towed rather nicely when empty, with the steering pinned.
Usually, though, I tow the truck. It seems there is always a need for it; something that needs to be hauled that won't fit in the PT! the truck MUST be towed four down or on a trailer. Dolly towing is not an option, unless the rear drive shaft is removed, which I do not want to do now that I have achieved 70+ years.