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.
I think that the responses that you recieve to this question will vary as to where the people giving them are from as I am sure this varies from region to region. Here in our center a full time seniority cover driver does not necessarily have the right to chose his/her run that they would like to do. They are only guaranteed to work before people with less seniority than them and I am sure that this senario probably varies from center to center also, we have a center that is approx 100 miles from ours and many things vary in how they are handled as compared to our center. The best advice that I can give you is to ask your shop steward if you do not like the response that you receive from your oncar sup or center manager and if that does not yield the results that you believe are due to you than keep working your way up the ladder starting with your business agent and so on..
UPS is going to make up the rules as they go along like they have always done. Bump or no bump they will put whoever is going to do the job first.
That is just my opinion and not a fact etched in stone.
let the other driver work and its one less day that your back will eventually go out.
It tells you this in the book.