Does anyone have an idea.. As a matter of fact yes I do, two or three of them in fact depending on your drop hitch.
The one/two are Blue Ox Hitch Immobilizers.. If your drop is a drop receiver adapter (has a receiver on the bottom) you need two, if it's a drop ball hitch) has a tong for a ball on the bottom) you need one. This keeps the hitch from wiggling, Go for the Blue-Ox, I have a knock off version I can give you but to be honest.. it is worth more as scrap metal.
Now, the real kicker.... This product will eliminate the sway.. Link is to the manufacturer's web page. Most RV dealers have it.. HOWEVER, i'm not sure how to mount it on your hitch adapter,, Well, I am but it takes an aircraft certified weld shop to be sure it's right or one willing to take the risk, many are not.
Reese Hitch Friction Sway BarIn fact, you will need to loosen the adjustment nut as this thing can stabilize over 2,000 of trailer with no trouble at all.