We also have a 2013 Parkliner
. Originally our camper had larger, bias-ply tires. When the tires-rubbing-on-ParkLiners issue came up I looked closely and found that mine were also rubbing ever so slightly. Ours also was towing poorly. I took it back to the factory and Chandler checked it out. When he designed the Parkliner he used the dimensions of the bias-ply tire. It turns out that the tire dimensions can vary somewhat between tires and he had evidently used a smaller example of the same tire to design the camper. He also had welded the axle
to the frame. This was counter to the instructions that the axle
manufacturer gave. Our axle
had broken down as a result. Evidently the heat from the welding compromised the internal rubber component in the axle. When I got the camper back it had a new axle bolted on and thereafter he said that all axles would be bolted on and not welded. He also had installed the smaller Nexen radiel light
truck tires. All of this was in the spring/summer of 2013. We have had no problem with the Nexen tires at all. They were on the camper when we towed it to Alaska in 2014 and gave excellent service up until March 2020 when I replaced the old Nexen tires with new Nexen tires. Very unfortunately the pandemic hit shortly after I got the new tires and the camper hasn't moved since. It will be moving shortly, however as we are ready to "hit the road."
I am not a tire expert. But I did look on-line at the rationale for putting bias-ply tires on a towed vehicle and the benefit seems to be that they can help minimize trailer swaying. With the radial tires we experienced zero trailer sway, better gas mileage and pretty nearly effortless towing. Some of that could have been due to the axle replacement. Anyway, my experience suggests that the small radial tires are not the only reason for your towing problem. Many things (for us, the axle) can contribute such as insufficient tongue weight
, unbalanced tire pressure, speed, and so forth. I would suggest that you take your Parkliner to a place that does RV maintenance and ask them what causes the issues you are experiencing. Hope this is helpful,