Great suggestion above from TheLittleYorkie on training to desensitize for an object. As Ann wrote too, many puppies grow out of it, with a little help. Teddy is still not enthusiastic about the vacuum cleaner, but he is fine if he can sit in one of the dog beds or on grandpa's lap.
I know what you mean about being so sad to see these little ones shake with fear.
For the gardener, I would try taking her outside (at a safe distance), even holding her, walking around and telling her happily what the gardener is doing, making your yard pretty. The sound of a reassuring voice can be helpful, and I'm sure you have noted how much language these little ones can learn.
