You could put a line from the outlet of the stock Trans cooler to an external cooler and then the outlet of the external cooler to the existing return line to the Trans. Don't think another fan is necessary
Keep in mind you are going to be very close to your max tow weight with that behind your rig. The Patriot is listed at 3273# curb weight (empty) and 4500# GVW. If you are towing it on a trailer or tow dolly you will need to calculate that in as well to your overall numbers.
3.7L is rated to tow 3500# and I am a big fan of keeping anything I tow under max rating by say 20%. If you are towing 1000 miles in the summer heat... be careful. A trans cooler and a trans temp gauge will be important. Does yours have the tow package already?
If you tow that on a tandem car carrier trailer you will be way over the tow limit for the 3.7 (those trailers weigh about 1200 lbs). If you use a dolly it will be close to being just at the limit or a but over.Make sure the dolly has surge brakes at least if not electric brakes.
Backing up is difficult with a dolly. I've towed with my WK and it tows well but the rear suspension is too soft.