Even with the tow package that thing is rated for 3500lbs MAX tow rating. By the time you put the weight of your car + trailer it will be close to, if not over, that rating. Without the tow package, which probably includes additional cooling and possibly different gearing, it’s rated at 1500 lbs.
It will probably pull it but expect a short life for your trans, shocks, struts, brakes etc.
Nice ride for the wife though.