The problem with your beloved Coton de Tulear is apparent due to the close proximity of your sidepipes to your dog's ears, hence my solution :
By securing your dog to the nose cone of your vehicle (Mack Truck style), pooch is forward of the exhaust noise. As a welcome consequence, any insecurity or anxiety previously experienced by your dog will be overcome with his newfound unrestricted view of where he's going.
If you have any concerns about wind buffeting, rest easy in the knowledge that the owner of this FIA will be getting just as much wind in his hair as the pooch.