Thank you all for your answers. Let me now answer some of your concerns. My problem is I have arthritis in my hands, not bad yet, but I do notice a difference from a few years ago.
I do not haphazardly handle my lines. I do not ever leave the cart without my lines in my hands. I never set my lines down. I am always mindful of where my lines are. I am not a novice driver.
Trust issue or not, as you all know anything can go wrong in the blink of an eye. Therefore I am as safe as possible when driving, that is why I asked the question in the first place.
I had a tip over in a hazard on a CDE several years ago, I avoided a very nasty accident having the lines with me as I hit the ground, as it happened, horse stopped, groom and I got back in the cart and finished the course. It could have been a disaster if the lines were tied, ever so slightly, to the cart. I forgot about that incident.
Thank you, again