Have your dealer check your axle alignment. If it's out of alignment it will bobble back and forth as the tracking is greatly offset. Check tire pressure on both your TT and your TW. Make sure the dealer installed your sway bars correctly as well. There are several issues that could cause the sway. A trailer is just a trailer and they all pull the same if properly setup. Failing any part of these issues could cause problems.
Good luck and keep us posted.
Chuck and Joanne
2014 Flagstaff Super Lite Classic 27RLWS Emerald
2013 Dodge 2500 4x4 Laramie Crew
Equal-i-zer 1200/12,000 4-point WDH