Primary causes to what you are feeling are:
1. Bow wave - A lttle push pull is normal. The hitch won't get rid of 100 percent. A lot of this is not normal.
2. Hitch not adjusted propperly, or underrated - If the hitch is not restoring enough weight to the front axle of the tow vehicle, you could have subconscious hand movement, which causes the truck / trailer combo to wiggle. Your 1000 lb hitch suggests, being under rated is not your situation. Scale weights will tell you about any adjustments needed.
3. Unbalanced loading, or, too light on trailer tongue weight - Scale weights?
4. Towing trailer with nose up attitude - Check hitch ball height.
5. Overloading tow vehicle - Check your payload. Subtract weight of all passengers, cargo, WD hitch, and actual trailer tongue weight, from available payload. If you're in the hole, a new hitch won't fix that. Passenger "P" rated tires have softer sidewalls than truck tires. It's possible, you're feeling sidewall flexing. You could spend a couple grand on a hensley and still have that problem.
Before you throw a bunch of money at a new hitch, check your actual weights, payload (everything and everybody's weight in or on the vehicle, count against this), tow rating, tire pressures, and hitch settings. Could be something simple as lowering the hitch ball, pumping up the tires, moving up one link in the chain tension, or re-arranging some weight in your loading. Then decide on if, or how much you want to spend on a hitch that may or may not improved your ride.