Kia Sorento KX2 auto 2016, caravan unsteady.

Have you tried increasing the tyre pressure on the rear wheels of the Sorento? It might help.

oddly enough my previous tow car, not a Sorento, but a 7 seat had a little picture in the door sill that basically said one type pressure for the rear and/or front for two people in the front, another set of pressures for middle seats used, and yet another higher if you had luggage/people in the boot. This meant that I should have pumped them up for towing then deflated once arrived on site then reflated after a few days... Needless to say I didn't do that, just kept at the higher set. Yes probably wrong I hear you say.

The sorento however has again these pictures but has the same tyre pressure for all of them no matter what or how many people you are carrying!

Don't know if this helps but the dealer knew we would be towing and set them for 37 psi, while the little pictures say 34 psi.

Also interesting is that in 6 months ownership they have not lost any pressure. I thought the in built tyre pressure monitor made be faulty or giving a misleading reading as it only works when the tyre have been moving for a few hundred meters but having doubled checked with a gauge when cold the monitor is correct.

One more thing, I've found that at higher speeds (for me anyway) the 'sport' steering mode is better than the 'normal' mode, called sports but all it does is dampen down the light steering and the car feels more precise?

I thought all cars had speed sensitive power assisted steering these days either by electrickery or mechanically. 

perhaps they do, but there is a notable difference in the two modes

 I've only had speed sensitive assisted steering that does it itself  ..... I've noticed though that even my little Smart Roadster's steering is heavy at slow speed when the electrickery part doesn't want to play.

Through use of Electrikery and other computer wizardry the settings can change the steering feel or feedback through the rim as well as increase the input speeds. However there are so many variables with the towing issue you have, could also be the tyres themselves, what brand and load index are they? A colleague had a 5 series with non runflat tyres on the rear and it handled like a pig when towing. Fitted o/e spec Continentals and the towing was transformed. I have just replaced Jinyu tyres on the rear of my Passat which although a budget tyre handled the Caravan fine and had an incredibly low wear rate. Today I will find out how it tows with Kleber Quadraxer. 

Kleber Quadraxer

Not a make Ive ever heard of .... 

I tow with the same vehicle, my van being 1700kg and never had even the slightest twitch, covering 3-4000 miles per annum. 

I had a 61 plate KX2 which didn't have SLS. Plenty of power but it never felt as good a tug as a previous Kia, a Sportage. Whilst the ride in the front was OK, rear passengers suffered car sickness. My grandson threw up twice in it. As for our two dogs in the boot, the oldest was occasionally sick although he'd been fine in previous cars, but the youngest was sick every time. She got so upset she didn't want to go in the car. I changed it and she's been fine since in two different cars and now is quite eager to get in.

I had Kumho tyres on mine, and after some ****** stabbed one of the tyres whilst parked outside work, when it was taken off the rim i thought the sidewall was very flexible, more than I would have expected. Higher tyre pressure might help or a different brand of Tyre.