Towing with a chevy cavalier


#1

I have a mint 2002 chevy cavalier(33,000mi.) with a 2.2L mfi L4 dohc (2200) engine with 4 speed auto trans. The manual says DO NOT tow with this engine. I want to tow a small tear drop trailer at 980 lbs. with a tongue weight of 95 lbs. will tow this just 80 miles twice a year on flat road in cool weather. I have also had installed a trans fluid cooler just to be safe. Do I need to still worry or will I be ok

Can I consider out or town trips at all?

Out of five engines chevy made for the cavalier why is mine the only one they say don’t tow with it?No weight in car except wife and I.No cooking gear,(we eat out), some clothes and thats it.please answer,hate to ruin my car.