Great idea to go to a homeopathic vet. They will understand the danger of vaccinations. They should offer to do blood titers, which will test the immunity of the dog. They should use things like nosodes as vaccinations, which is homeopathic. All of this is very good. They should also explain all of this to you when you go.
As far as the fear of the rain goes, can you think back to the first time it happened and possibly what your reaction to it was? You may have accidently given the dog a psychological signal that has caused a nervous or negative reaction to the rain. If you always act like the pack leader with calm assertive energy this will be transfered to the dog. (Try watching the Dog Whisperer, who is Cesar Milan, on Discovery channel - he uses dog psychology and fixes these type of things instantly.) Is it possible to try to desensitize the dog now using a hose as "rain" and make sure that the dog isn't being coddled or rewarded for the fearful reaction when it is refusing to get wet? You don't want to reinforce the negative reaction to the rain, but take the dog confidently out in the rain (or hose), so the dog picks up on your confidence and learns that rain is no problem. This will take some work, but can be changed to a positive.
Your vet should have some good ideas about this issue as well.