Sounds like you have a couple problems potentially must importantly your tongue wieght. With a 3500 dry wieght trailer and assume at least 500# (your probably more) you need at least 500# of tongue wieght. Go a scale and get wieghed, figure out what your true tongue wieght is
- With 4000# plus of trailer you are pushing the limits of your vehicle so some of the problem maybe suspension
- Your vehicle probably has P metric passenger tires pushing thier limits. This will cause some tire side wall flex will feel like sway
Good luck but I suspect you fix the tongue wieght and WDH balance and it will improve greaterly
