Hello Estelle,
Do you know if Mary's name was possibly Mary Magdalene Miller instead of Mills, and if she was married and had three children? I made a posting on ancestry.com years ago regarding a family member of mine who appears in some sort of Russian military uniform asking questions about his background and any help with identifying his uniform. While I am not sure if I have the right person, I was informed by another user that the man's name might be Michael Kautzmann and his wife Mary Magdalene Miller due to the similarities that myself and this other individual had in our family stories. While I am not sure if Mary was a nurse, or how much contact she may or may not have had with the royal family, she was married to a Michael Kautzmann who served in the Russian military. After they left Russia in 1899 they settled on the West Coast of the US. Please let me know if you think this sounds plausible, if so I would love to research and see what we could find.
Best,
Sarah
P.S. I emailed you as well.