Most dogs are not great fans of going to the vet, in some cases it can be a real problem but that behaviour can be changed.
Make time for some fake trips to the vet. Drive some way towards the vets and park the car, get out and put the dog a lead. Now go for a walk rewarding your dog for good behaviour, do this several times.
After a few walks, extend the route so you go past the vet’s surgery, again rewarding good behaviour. It’s important to make the rewards special, maybe some chicken or other treat that your dog really enjoys but doesn’t get too often. The aim is to turn the dog’s perception around, to make the “bad place” into a “good place” hence the need for frequent rewards.
When your dog can comfortably walk past the surgery, try going in and just letting him or her just look into the waiting room (at this stage it might be better to inform the surgery of what you are doing).
Final stage, go into the waiting room and sit quietly and then leave and go home.
Each stage must be repeated until the dog is absolutely comfortable and showing no signs of distress. If at any point the dog is getting upset, go back to the previous stage for a little while.
All it takes is a little patience and a visit to the vets can be a lot less traumatic for your dog and you.