"The car isn't going anywhere" Or words to that effect. You must really like the car... I have car I really like too,,, so I know how it feels. I keep it waxed and maintained religiously. I love that car. I wouldn't do anything with it that was not good for it.... And that means no towing with it.
As stated by others. The 3800# rating of the hitch is meaningless. Many pickups use the same hitch with same rating, yet the pickups tow ratings vary. Your owners manual is your bible.
A hitch with a higher rating than the car, doesn't make it a "unique configuration" that magically almost doubles the tow rating.
Your tow rating is 2000#
Deal with it!