Would the older Jeep Liberty model meet your looks requirement? If so, I believe that could tow a Casita/Scamp type TT.
If you must have the Patriot, don't buy more than an 8 foot popup camper (basically two double beds, a sink and a dinette). And even that will be a heavy load requiring careful driving.
I'm not one to say "y'all can tow nuthin' without RWD and a frame" but there does come a point at which the wagon needs a bigger horse. The Patriot has a small engine and a short wheelbase. It needs a really small trailer at most. A Coleman Taos popup would fit the bill (no built-in toilet though!).