You didn't mention the year or mileage of your Precept 35UN. Assuming it is new, then suspension wear and bad shock absorbers can probably be ruled out.
Before adding components, make sure they are really needed:
FIRST make sure that your tires are inflated at or near their maximum, like mowdoc did. Then take it for a drive. Often that simple step makes a world of difference.
SECOND, find a good alignment shop, tell them about your handling issues, and have them align it. Often they can make adjustments within the specifications that improve handling.
The 'CHF mod' will not change the alignment settings so try that if the first two didn't help enough.
I drove I-40 & I-44 from Flag to St.Louis twice this spring; once just the TV then with the TT. No road issues. The only problem was the weather.
Sherm & Terry w/rescues Steve (std Poodle) & Eydie (min Schnauzer)
2015 Jay Flight 27RLS (Camped: 102 nights 2015, 90 nights 2016)
2006 Ford F350 6.0 PSD, Lariat, 4WD, CC, LB, SRW, auto., Camper pkg.