I agree with Jerry; it's not a good idea for several different reasons. Not the least of which is how that hitch was designed or attached. Most receivers on the back of trailers are designed to hold little more than a bike rack; they are not "tow rated".
You also have to consider length restrictions. Granted, I've seen plenty of tandem rigs that were obviously in excess of our limit here (65 ft), but IMO, those are there for a reason. With the length of the truck, plus 36-1/2 ft of trailer, plus the tackle for towing, plus the length of the Challenger, you're probably well in excess of 65 ft.
Then there's the cost of actually being able to tow the Challenger; base plate, tow bar, wiring/lighting, brakes, miscellaneous towing tackle... You're looking at over $3K to do it right with good equipment.
Then there's weight. Can your truck handle the GVWR of your 10,000 lb trailer, plus ~4500 lbs of vehicle hanging off the back? All added to the weight of the truck itself?