Use your riding lawnmore. Lawnmower wont be carying any weight
, it only push/pulls the trailer since its tounge wheel(s) will be down.
you might want to install a second wheeled trailer tounge jack.... or install a jack much more heavy duty than your trailer requires. This way it will be less prone to break as you jocky it around.
Go to your local welder and have him weld you up a frame on your riding lawn mower with say a female reciver tube on it. Then have the welder make you a push bar AKA a longer; (3feet), male reciver tube and mount a ball onto it.
Hook up the two together and push the trailer around to your hearts content.