Was this the first time you towed the trailer with the motorcycle in the truck? That could cause a difference in handling.
Was this the first time you towed the trailer with the new tires. New tires have been known to cause a significant change in handling.
If the new tires are the cause of what you're experiencing, the problem might resolve itself after you get a few hundred miles on the tires. Or, you might not have the right amount of air pressure for the new tires.
If the motorcycle is causing the problem, you might be able to confirm that by towing without the cycle. How much does the cycle weigh?
How do you have your weight distribution hitch adjusted? Did you increase the load on the WDH bars to attempt to compensate for the added weight of the cycle? If so, the additional load transfer to the TV's front axles, could be causing a change in handling?
Ron