You say you're using an anti-sway hitch. It should dampen side-to-side "fishtailing" motion but not bronco action. I assume you are also using a hitch with weight equalization (torsion, etc.) bars. Maybe your bars are not tight enough... meaning they are mushy and are not transferring enough weight to the tow vehicle.
Edit: do you have a pic of the hitch and tongue from the side?
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Nights Camped: 2013 = 49 / 2014 = 74 / 2015 = 74 / 2016 = 74 (booked = 11)
FR Wildcat 295RSX / GMC Sierra