Once upon a time (about 1985), I rented and towed a fiberglass U-Haul CT-13 camper trailer on a 2,000 mile vacation (MI to CO and back) with a 1984 Dodge Omni. 2 adults, 2 kids in a car with less than 100 HP. I kept it mostly under 50 mph (55 was the speed limit back then anyway). We had a memorable vacation. Worst thing that happened was, the front window leaked in rain and got the kids' bedding wet.
Somewhat older and wiser now (having towed trailers of various types and sizes for several hundred thousand miles), here are my thoughts.
First, the Mazda should be capable. Curb weight is probably about 3600 lbs with about 800 lbs of payload; that includes gas, gear, driver, passengers, and trailer hitch. Assuming youngish kids in back seat and if you don't load too much gear for the trip, you should be able to stay under the limit.
Second, the bulk of the frontal area is the trailer body, so use a tape measure and check it, then add a bit for wheels and axle; you might be a little over "book" spec but if you keep your speed down you'll be okay. Wind resistance increases exponentially with greater speed (it's not a linear increase like one might think).
Third (most important), make
certain your hitch weight when loaded is between 10% and 15% of total trailer weight (you can use a bathroom scale to check this), because an improperly loaded trailer can cause it to sway dangerously. In my early towing days I once had frightening, uncontrollable sway with a 4'x8' utility trailer (!) because I had
negative tongue weight due to a steel part hanging out the back end.
Fourth, consider adding an auxiliary transmission cooler to your car. But whether you get one or not, be sure to lock out overdrive if possible, because when the tranny 'hunts' between high gear and the next lower gear (you'll see the RPM rise maybe 500 but it hasn't actually shifted) it's letting increased friction generate a lot of heat in the torque converter.
Fifth, if there are backer plates (square metal plates with holes near each corner) behind the wheels, the axle will accept a trailer brake kit; in that eventuality, I'd get some trailer brakes added, buy a Tekonsha Prodigy brake controller for up front, and wire the connection with the 7-pin plug. I would
not go with a surge brake because I consider controllable trailer brakes to be a very useful safety feature. Not just for stopping, but also to help counteract sway if you ever did have it (let's say some trailer contents vibrated backward during travel, changing the balance?); using the brake controller to apply trailer brakes while
slightly increasing speed (counterintuitive but correct) can help bring the trailer back into line. And if you have a deer or a dumb driver jump out in front of you, trailer brakes might make the difference between a messed-up front end vs continuing your happy vacation (after changing your shorts).
Stuff happens, be prepared.
In short, don't despair, all is not lost. A few thoughtful precautions in advance and you should be good to go and make some nice family memories.
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