My first question is : are you sure your dog is vomiting because of the medication?
I noticed you said your dog has already been on this medication for a few months. I think that is kind of a delayed reaction don't you? Perhaps it would be a good idea to ask your vet this question. It is possible that there maybe another thing going on with your pup.
In the meantime , I certainly don't disagree that it is always a good idea to reasearch other safer alternatives for your dog's treatment of arthritis. I would get on the internet and research arthritis in dogs. I promise you once you get on the right track you will learn so much! It will help you ask the intelligent questions needed (to your vet) that will eventually help you decide whether he is well informed enough about the illness or too close minded to assist you in doing what you feel is best for your dog.
I wish you much luck and hope you keep us posted on how your baby is doing...Take Care...Scout