Just started full timing a few months ago & Im tired of the sway & wobble. We used our last TT so infrequently it wasnt worth it, but now with 2 adults, 2 kids, 2 big dogs & 2 small dogs we almost ...
The only way to stop all motion is get the wheels off the ground and put solid blocks under the frame about every 4 to 6 feet.
Braces such as JT's Strongarms will help, as will X-Chocks between the wheels on both sides.
One thing we have found is the heavier the trailer, the less rocking. Also, put solid blocks under the jacks and stabilizers and extend them as little as possible.