It sounds to me like perhaps your truck is riding on the overload springs when hooked up to the trailer. That would account for the rough ride when loaded.
I would take a look at your weight distributing hitch setup. Get the truck and trailer weighed when loaded so you know exactly what your tongue weight is, and then set up the hitch accordingly. I suspect your tounge weight is much higher than you think. Your truck should ride better when the trailer is hooked up - not worse.
There is a good possiblity your hitch is either undersized for the load or is not set up right. You most likely need stronger WD bars or need to raise them higher to transfer more weight forward to the front axle of your truck and remove it from the rear axle. There should be no need for the air bags if the hitch is sized and set up properly.
Take a look at the
hitch set-up sticky at the top of this forum for some help.
Barney