Either the Reese Dual Cam or the Equalizer will do you fine for a Bambi 19' behind a Yukon. The HA is a superb hitch, but won't do any better job controlling a trailer of your size and weight than the other two, and it weighs significantly more.
Sway is caused by inappropriate weight loading, tongue weight that is less than 10-15% of the total load weight, low or unbalanced tire pressures, and either warn suspension parts or good ol' design flaws in the suspension on the tow vehicle. Once you eliminate those as causes of sway, your trailer shouldn't, and your sway control hitch will just be an added measure of safety.
Thanks. I appreciate the positive reinforcement. It boosts my confidence in my TV.