My first thought was gotsmart's suggestion re: QuietHitch. Eric Davis is an RV handling guru (along with the Henderson clan and a few others) and he warned me there cannot be looseness (such as any form of side play) in the Toad/Baseplate/Towbar/Drawbar(including Drop/Lift Adapters)/RV Hitch. Said as much as 1/2" will cause the toad to bump-steer the rear of the RV.
Is your C on a Ford E350 chassis? And, what is the Wheelbase? Our 24-ft C was on E350 with 158" (a stock wheelbase) and rear frame extension for a bumper-bumper length of 25-ft. Heaviest toad we pulled was 2500-lb and it did not detract from handling.
If there's not looseness in your towing rig, I have another suspicion. That your C might be right on the cusp of a handling problem and the toad pushes it over. I did VERY few things to the E350/460/C6 Chassis/Engine/Transmission setup.
1. I found the front sway bar end link bushings were shot. All but nonexistent. Replaced with a kit from NAPA that turned out to have hard black poly bushings. Again, end links only. I never changed the center bushings, and the change with good end links was stunning. With swing axles, side/side interference at the rear will try to raise one front corner and lower the other. That will cause it to "steer" and you don't want that. A tight sway bar will help.
2. I found the front end was Toe-OUT by a good amount, and adjusted it to a slight Toe-IN. THAT change took it from White Knuckle/Elbows on Knees driving to try and hold it straight, to an Easy Driving Vehicle. Easier in fact than out later E450 (Signature).
3. Replaced Steering Gear Box. It seemed to have play and when I adjusted that, it started to leak so I installed an AutoZone reman box. I don't really think the steering box was that much of a problem.
4. Replaced front shocks with Monroe RV Gas Magnum. Did that When...
5. ...I replaced Front Axle Bushings. That was the two where the swing axles meet the crossmember (one on each axle) and the two Radius Rod Bushings (those shafts that angle back to the frame). Not sure that was absolutely necessary either, but I saw an E350 van that wandered all over the road with bad swing axle bushings, and could also tell that if the Radius bushings got soft, the steering would Toe-OUT.
Most of what I did was plain dirt cheap (providing my own labor of course) and I never took it to an alignment shop. Results were stunning as I mentioned.
I replaced tires too. 8.75R16.5D, and ran at 55-front, 65-rear. If your fronts are at a higher pressure than the load calls for, tracking is compromised.