Really Grandman? The trailer was a full half a ton UNDER the rating for the H3. A good Prodigy brake controller, appropriate load leveling hitch with sway helper and it's no problem at all. In large part, the stability of a tow is in the weight and stability of the tow vehicle. The H3 is HEAVY, rigid, and super stout for it's size. This is no unibody with a hitch stuck to the bumper sub assembly here, this is a Hummer H3 with a frame, substantial rear springs.
I think a 3000-3500 lb. travel trailer is WELL within the rating for the H3.
I've done some hairy tows before.
A 10,000lb container/trailer on a hitch, no load leveler. It was horrible. I'd never do that one again.
My boat for miles and miles and miles. It was about 6,500 lbs loaded with fuel. Heavy, and only had a surge brake. The boat and trailer almost outweighed my truck!
My car hauler with various loads behind our truck and Yukon. 7000lbs, again, no special hitch. It towed like a dream, great brake controller.
That H3/travel trailer scenario is safe.