When am I entitled to pay?

I work for a firm in Memphis Tn. In my job responsibilities I have to drive a company vehicle to my work site which located 1.5 miles away from where the vehicle and keys are kept off the clock. The keys are kept inside the company warehouse. In order to access the keys to the vehicle, I have to wipe in with my ID card at the warehouse. The warehouse is where other employees that don’t have to make the drive that I do clock in and out. After I drive to the site I swipe in again. According to company policy l have to swipe in again at the site and that second swipe will determine when my compensation begins.
I feel that my duty hours should begin when I clock in at the warehouse office. If my duty hours don’t begin with the first swipe, my employer can’t compel me to drive the company vehicle until my actual start time begins. Also I can’t be reprimanded for refusal to travel to the work cite before my actual scheduled work time begins.
Your opinion please