Hopefully, I have learned enough from all of you to not make too many mistakes.
My trailer hitch came off a one-ton Chevy van. The sticker on it says: "6,000 pounds towing weight; 600 pounds tongue weight". It was narrowed, and new brackets and supports were added. (Only tack-welded in first picture.) It was fastened in two place on each of the frame rails, and not the engine mount.
The guys at the welding shop did a very precise cut in the stainless bumper to clear the trailer hitch.
The possible toad (Hyundai Verna) weighs about 2,400 pounds. The little trailer under the car I am guessing around 1,600.