:S I cannot believe the number of people who have said that a WD hitch will help. It will not!!! The hitch weight was already too light, so redistributing some of that weight to the truck's front axle will not help one bit!
What people should have said (and a few did) was that an anti-sway hitch can help. Something like an Equal-i-zer (someone did mention that brand) or Reese Dual-Cam, a WD hitch with sway control built in. Or even a sway bar or two would help somewhat.
However, putting sway bars or an anti-sway hitch on an otherwise unstable rig is like putting a band-aid on an infected sore. The OP needs to address the root problem, first and foremost! Find out what the hitch weight is when the Rhino is loaded. A safe hitch weight is 10% to 15% of total trailer weight. Add weight to the front living area until the proper percentage is on the hitch, and this trailer will tow well. Then add the anti-sway hitch or sway bar(s) for added safety assurance. But if you cannot add enough weight to the front (say, it puts you over the CCC of the trailer), then you simply cannot carry the Rhino safely in the trailer... band-aids or no band-aids.
Also, be aware that you never, ever want to hit the brakes sharply during a sway event (not saying the OP did so, this is just FYI). Instead, use the brake controller in the cab to apply just the trailer brakes, and hopefully this will bring the trailer back under control.
I don't care what size trailer a person tows; a proper hitch weight is vital to proper safe handling characteristics. Once when I was young and foolish, I had negative hitch weight on a little 4'x8' utility trailer (about 11' overall length), and near the end of an uneventful 3 hour drive it started whipping around violently and scared the snot out of me. Laws of physics don't just apply to the big trailers, but to small trailers also.