The best way to introduce one dog to another is to pack-walk both dogs. Meaning, both dogs are walking together and heeling on the lead. This sends a signal to the dogs that they are not in charge; the humans are in charge and they are to follow the humans. I realize you cannot pack-walk your dog with all dogs you come into contact with, but consistently pack-walking your own dog will communicate to your dog that he is following you and looking to you for commands rather than the other way around.
You should be going through all doorways and gateways before your dog as well, especially at the vet, and the dog should be heeling beside you while you walk him over to your seat. As soon as your dog begins to see you as someone to follow, he will respond to your corrections much quicker when you tell him to leave the other dog alone by giving him a tug on his lead and/or a verbal command.