Mary, her children Elizabeth, Almus, Mary, Georgina and Thomas sailed to America in 1863 on the ship Cynosure. Their surname is spelled "Park" on the ship.
Evidence from emigration and genealogical records proves the Parkes family traveled to Utah in 1863. Further research is needed to determine the name of the company they traveled with.
Her surname is "Miller" on the 1870 Utah census, her burial records and Find A Grave website. Her husband died in England and when she came to Utah she married Thomas Miller.