Not a towing expert by any stretch, but what type of tongue weight are you trying to pull? Looks like the trailer may be too heavy at the tongue.
Two possible options, relocate the spare to the trailer so you can eliminate the extension, or I believe that Road Armor made a replacement rear bumper. Some have posted fittment issues with the RA front bumpers, but not sure about the rears.
http://www.roadarmor.com/site/hummer/
Chris