I cant imagine towing with the MH being an issue for the horses. The Palazzo has a 6.7 Cummins with rear exhaust, just like several hundred thousand Dodge pickups that tow horse trailers every day. You can always buy an inexpensive C02 logging detector and put it up front where their heads would normally be. Test drive it around town and on the highway to see if there are even any detectable levels of dangerous exhaust.
My covered car trailer is a 27' double axle unit, roughly equivalent to the 3 horse trailer I had back when I owned pasture ornaments.
At the very front of the current trailer there is a work bench with drawers and cabinets below/above and toolboxes on the work surface. Our last race was in Hastings, Nebraska. When I was buttoning down the car before heading for home (Denver area) and I accidentally left my 1/3 full plastic cup of Coke sitting on the workbench. 8 1/2 hours later when we arrived in Denver, it was still sitting in the same spot with a few small splashes on the work surface. So it couldnt have bounced that much.
Lay on your master bed while someone else drives the rig to see how much it bounces. Depending on the length of the trailer tongue it will also mitigate some of the movement. It is probably impacted a lot more by the suspension of the trailer itself and how smooth it is.
My Palazzo brakes are not jerky, they're pretty smooth as long as the brake controller for the trailer is properly adjusted. They just take a looong time to stop so slow down a bit a give yourself plenty of safety margin.