If I'm thinking about this correctly and the wheels on the dolly actually turn (like a farm wagon) then it's not going to matter if the steering of the car is locked or not. The rear of the car is going to naturally follow the dolly. I know the OP said the empty dolly tracts good but it would be hard to tell if it was perfect IMO because the dolly is so short and no straight side to compare with the MH.
OP, if the rear alignment checks out on the car is there a possibility the alignment could be out on the tow dolly?
Edit, no because the car would still run straight with the dolly, the whole car's centerline (from to back) would just run offset to the MH's centerline. You are saying it is running skewed to the MH Right? That would be misalignment of the rear car's tires.
