There is a Volkswagen repair shop in my town but I have not been pleased with their service in the past. I am wondering is it necesary to bring a Volkswagen diesel car to a Volkswagen mechanic or can other mechanics work on them?
A qualified diesel mechanic or mechanic that’s familiar with diesels should be able to work on any diesel vehicle. The question is if they will or not.
I suggest you log onto TDIclub.com. They are the spot for VW Diesel information. They have a list of TDI mechanics and likely there is one in your area. You will also find lots of information if you are interested in doing some of the work yourself.
A qualified diesel mechanic or mechanic that’s familiar with diesels should be able to work on any diesel vehicle.
That can be untrue for at TDI. It’s computer system is unique to VW’s and requires a special tool to access that system, which among other things is used to set the timing.
It’s interesting that you would say that the question is whther they will or not because I brought my early 80s diesel Rabbit to a repair shop to get it analyzed to see what kind of shape it was in and they referred me to the Volkswagen mechanic. I am not sure why the shop wouldn’t do the work themselves. Why do you suppose that is? 
I agree with the suggestion about TDI club. Folks that work on truck diesels aren’t going to be very interested in your VW, you want someone with VW diesel experience.