The Stone family emigrated from England in 1848. They sailed on the Sailor Prince, and arrived in New Orleans on 20 November 1848. It appears that Samuel Stone died sometime after arriving in the USA. According to the Missouri Marriage Records, Hannah remarried on 21 July 1850 to a John Bardsley. Hannah (Anna), two of her children, Jane and Jacob, appear in John Bardsley's household in the 1850 Missouri Census.
According to the 1856 Utah and 1860 California Censuses, John and Hannah had four children between 1853 and 1855. Three were born in Illinois, John Jr. (1853), twins Olive and Susan (1854), and Thomas was born in Utah (1855). It is likely that they came to Utah in 1855 before Thomas was born. Church ordinances were performed for some family members in February 1856, and the oldest daughter, Jane, was married that same year.
Further research is needed to narrow down the company they traveled with.