Your daughter’s dermatologist, especially with the opportunity to visualize these lesions, would be the person best able to make the correct diagnosis. Perhaps the first step should be to allow him to re-examine these lesions, when time constraints would not limit his exam.
You mention hand-foot and mouth disease. That would be a reasonable consideration, especially were your daughter also to have a slight fever and vesicles on the tongue, pharynx, palate and/or lips. It should be noted that this particular vesicular rash may complicate pre-existing eczema. Another skin disease that might present in this fashion is Pompholyx (dyshidrosis), a condition that presents with a distinctive pattern, with symmetric vesicular hand and foot lesions.
It is extremely unlikely that these water-filled blisters are related to vitamin administration. Once again, the dermatologist would be the best person to rule-out “immune boosters and probiotics” as an allergic cause of your daughter’s skin lesions.
If all her current doctors remain puzzled by these lesions, you might want to request a second dermatologist opinion.
Good luck.