You're the second one today who has posted on this issue. You're not alone. Be sure to read the responses in the other thread, they may help you:
https://forums.goodsamclub.com/index.cfm/fuseaction/thread/tid/29388792/srt/pa/pging/1/page/1.cfm . My comment to him is on page 2.
Simply put, you
must find out your actual trailer weight and trailer tongue (hitch) weight. Hitch weight needs to be 10% to 15% of total trailer weight as loaded for camping. Sway is almost always caused by insufficient hitch weight.
Don't go by "I think it's pretty balanced," you must
find out for sure what those weights are. Once you have made sure of correct hitch weight, you can further enhance handling by making sure all tires are inflated to max pressure as indicated on their sidewalls and by having the trailer slightly nose-down when hooked up. And you can increase your safety by adding a good anti-sway hitch such as Equal-i-zer, Reese Dual Cam, or Andersen No-Sway. Or at the very least, get a friction sway bar... but I'd recommend the Andersen for any trailer under 3500 lbs or the Equal-i-zer brand (from Progress Mfg) for heavier trailers.
I put 140,000 towing miles on a 2008 Highlander without incident. Trailers were 16'-17' overall and ranged up to 3500 lbs and 425 on the hitch. You should not have to suffer with sway.
Anyone at all can check to see if the controller is activating the trailer brakes and if they're adjusted well, it's easy. Drive about 10 mph and activate the controller; you should feel the brakes slowing your rig down (eventually stopping it gently) but not locking up the wheels. If you feel nothing, turn up the controller power (read your manual, there should be a dial or something). If all the way up and still no braking, it could be a broken wire or a defective controller, but first thing I'd suspect is that the magnets in the brake drums may have stopped working.
There is a slight possibility that you may have a broken weld on the frame or loose u-bolts on the axle, something like that. The way it happened when you hit a dip makes me wonder a bit.