A sway should have happened to anyone who tows a car trailer... if you haven't driven through it you can't appreciate that moment of terror when you think "oh F&^k".
It's only happened to me once or twice... my wife was driving once. Towing a tandem with a Pursuit on it with a 5.0ltr EF Fairmont. She had the power on hand to pull it straight (which did work very well for us I might add) and she had to sort it out several times on our 30km trip. When we got home she had aching shoulders and arms from being tense the whole 30 min trip lol.
Anywho, pull your towed car up enough to sink the backside of the tow vehicle an inch or two and see how she travels - if it isn't right, either travel at a safe speed or stop and sort it out.
Ahhh the terror
