When towing the RV, I'm just under the combined weight limits, using LT Load E tires on the vehicle and trailer, have WD hitch along with an anti sway brake, tongue weight is within range, and the trailer is longer than yours. Expedition has the tow package. Just about any aerodynamic-brick type vehicle pushes the combined rig around a bit when I get passed. Semi's to Jeeps.
Am suspecting that this is just a fact of life with an independent rear suspension when it tows in the upper range of its capacity.
If you need even less movement, go with a 3/4 ton vehicle as the ones I had previously used did not care what passed them and were more stable when towing. A current F150 might work better as it has a solid axle, but I do not have any experience with it. There are used 3/4 ton SUV's out there, but they are long out of production, hard to find, relatively expensive, and sell quickly.