If you can flat tow your truck, I think you'll find that works out better.
Flat towing, you have a tongue weight of about half a tow bar on the motorhome, or practically nothing. Towing on a car hauler, you have ten percent of the truck plus the trailer weight, or several hundred pounds. As this is applied well in back of the rear axle, you'll likely be adding something like 700+ pounds to the rear axle of the RV and reducing the load on the front axle by maybe 300 pounds. That is assuming your hitch is rated to take that much tongue weight; often class C motorhome hitches are not rated for as much tongue weight as the overall tow weight rating would usually imply.