There aren't any truck stops in Durango that I recall. Nor can I think of any good places to drop a trailer for a few hours. However there is a Walmart and a Home Depot in town. While neither (I think it is by city ordinance) that there is no camping overnight at either however just dropping a trailer for a few hours might be totally doable as I see rvs in those lots frequently. Perhaps a call beforehand to the Walmart manager would be in order.
http://www.downtowndurango.org/parking. You might also try calling some of the local campgrounds and see if they would allow it. I know one of the KOA's we use occasionally around here will let me leave my trailer in their storage/overflow parking area if I am going to be later than an 11am departure so as not to incur an extra day rental (I know?? too long of a set of circumstances to get into why I would need to do that but I have and doing it again this weekend)
Also if in Mesa Verde perhaps you could spend another night there and drive that trip from there making a loop go to Durango, Silverton, Ouray then left on to HWY 62 at Ridgeway, up over Dallas Divide to Placerville then another left on to 145 then into Telluride, Rico, Dolores, Cortez and back to Mesa Verde.
