For whatever reason they do tend to rock from side to side a bit.
Most of our side-to-side motion comes from people entering /exiting the trailer. The steps stick way out from the side. So I've put jacks under the last step; they help quite a bit.
Perhaps jack stabilizers going across the trailer would help also:
JT's StrongarmHave already reduced up/down motion by strengthening the arms so I can really tighten them up without bending them.
Have reduced the front to back motion with between wheel chocks.