Need Advice on Sway

I dont think you are unable to take the scooter, but even though your excursion is based on a full sized truck frame understand that your wheelbase is almost identical to a F-250 Regular cab short bed truck. Length is your friend, just as tongue wight on the trailer is your friend. The 35' trailer with only a 11% load on the tongue combined with a tow vehicle that was on the short side combined to make your attempt harrowing. You could add weight forward, Maybe an additional battery and make it a big one, as well as shifting some items from the rear of the trailer forward to effectively gain the additional weight twice, (off the rear and added to the front) as a means of regaining control. Be careful though, that model only has a CCC of about 1100 lbs, which means you dont have much room to work with.
Good luck