What legal rights do I have if a uhaul agent attached a car dolly improperly to my car causing damage?

You can sue U-Haul for negligence.  An employer is liable for the negligence of its employee which occurred during the course and scope of employment.  The principal (U-Haul) is liable for the negligence of its agent.

Negligence is the failure to exercise due care (that degree of care in this case that a reasonable rental agent would have exercised under the same or similar circumstances to prevent foreseeable harm).

In order to prove negligence, you will need to prove duty (of due care mentioned above), breach of the duty of care (failure to exercise due care), actual cause, proximate cause and damages.

Actual cause means but for the U-Haul agent attaching your car to the dolly, would your car have been damaged?  If the answer is no, which appears to be the case, actual cause has been established.  Proximate cause means were there any unforeseeable , intervening acts which would relieve the U-Haul agent of liability?  If the answer is no, proximate cause has been established.  Damages means the amount of compensation you are seeking in your lawsuit. Your damages would be the cost of repairs to your car.  If you need a rental car while your car is being repaired, the cost of the rental car should also be included in your damages. You will need to mitigate (minimize) damages by selecting a repair shop whose charges are comparable to other repair shops in the area.  If you were to select the most expensive repair shop you could find, your damages would be reduced accordingly.  You will also need to mitigate damages when selecting a rental car.  if you were to select the most expensive rental car you could find, your damages would be reduced accordingly.

Prior to filing a lawsuit, it may be possible to settle the case with U-Haul's insurance carrier.  If the case is settled with the insurance carrier, NO lawsuit is filed.  If the case is NOT settled with U-Haul's insurance carrier, you will need to filie your lawsuit for negligence against U-Haul and the agent prior to the expiration of the applicable statute of limitations or you will lose your rights forever in the matter.