I tow with a 2014 Santa Fe, previously has a 2010 model. I'm no expert having only towed with these 2 vehicles but reckon the later model tows better. feels more stable and a more relaxing experience. Not a massive improvement but noticeable.
Have towed from Bournemouth to Cornwall and both tackled the inclines without fuss or drama (both up and down). I've read the review you posted a link to and didn't feel lane changing or sidewinds were an issue but then I haven't got anything to compare it to.
The later car has a stability assist feature when towing.
My wife was a nervous passing (when towing) in the earlier model but is relaxed in the 2014. I've covered 14,000 miles in the first year with no issues and love the car.
I bought a 2006 2.2CRDT with only 32000 miles, had it 2 years, and was the most expensive unreliable car I ever owned. The dealers are hugely expensive, I took to importing the required parts from the US.
Shame really as when running ok was a good to drive with lots of storage.
My recommendation is either a Land Cruiser or Pathfinder.