The dolly and car will only provide a certain turn radius. It's not great but when managed well, will do the job. Try to work with the dolly and only use what it provides. There are some variables. Width of the dolly and width of the car are the two factors to be considered. Whether the vehicle is centered will also change the radius on each side.
The swivel platform is primarily a relief for the mechanics of the dolly and car for the turning radius. I had not thought of that option as having a positive effect on the amount of turning radius provided although it may provide some positive amount. How much, if any, I am not sure.