Short wheelbase!
I tow 6000+ boat trailer for a 28' boat with my Escalade (which is even shorter wheelbase than the H2). At speed it will sway a bit no matter what. Just need to concentrate when you drive and keep it straight and don't make sudden steering changes. There is no comparrison when towing with something like an F350 or anything with a longer wheelbase. They are made for that.
Yes, the H2 is not designed to be a full time tow vehicle, but it will do the chore when needed.