Yes you have every right unless it's a training route this driver is on. No matter what UPS tell you just remind them it's all about seniority and hand that other driver a map.
IMO I always learned better on a cold route than having a sup ride with me. Just remember its not your fault that this other cover driver doesnt know the route. Make sure you put in on paper Friday that you would like to run x route next monday that way your covered. Make sure you dont bump off that route during the week bacause we were told you cant go back no matter what.
I would have your sup sign this paper saying what route you want to run for next week, stamp it with your union clock, and always make a copy for your records and keep.
Good Luck