That's wrong. I would take it in to Tesla. That is definitely a liability issue they will want to correct. My CT stays exactly in the center of the lanes. Yours should too? Somethings not right there.
When you put in the destination does the GPS account for the reduced milage because you are towing? I would assume it gives you closer charging stations?
I reserved a 39k CT 4 years ago but turned down their offer for a Foundation series. Then I was offered dual motor for 79k and I took the deal. It was the best thing I ever did. More fun than all of my previous vehicles put together and I’ve owned many.