Boy, can I relate to your issue. I now am sure to have either my small dog's vest, emblem, bandana, or large medical service tag apparent. I also always carry copies of both her certification and my psychiatrist's letter in case I have issues.

My own disability is "hidden" as you say, until such moments when it is not. Then, like you said, they all get to see why Luci Sky is a service animal.

I wish you luck with this and advise, like in the other reply, to carry documentation or have your dog wear obvious service dog paraphenalia. (or both) The prejudice and ignorance of some of the general public will never be resolved, but we have to exude confidence and maintain our rights under the auspices of the ADA. We too have rights and must demand (politely) respect.