Records for Aaron vary on the spelling of his name. His children split about half and half between the Crosthwaite and Crosthwait spellings. The gravestones of he and Francis use the shorter spelling.

Her gravestone has her birthdate but not her death date.

Records from the 1850 census onward, including the birth record for Aaron’s son Turner, are fairly consistent that he was born in Lawrence Co., Alabama. But land transactions in Alabama and in Clark Co., Ky, suggest that his father Asa did not move from Kentucky to Alabama until the mid 1830’s. So it may be that he simply considered himself to be from Alabama because he spent his formative years there.

In 1850 Francis was recorded twice, once with her parents in Bath Co., Ky, and once with her husband in Alabama. Aaron was recorded only once, in Alabama, and their infant daughter Rhoda only once, in Kentucky.

1850 census of Bath Co., Ky, division 2, enumerated 15 Aug, lists as family #462:
Margaret Piersall, 68; John Piersall, 38; Thornton Piersall, 23; Francis Crosthwait (f). Margaret born in Virginia, all others in Ky.

Their oldest daughter Rhoda is in the next household (#463):
Reuben Willson, 23; Mariann, 23; Franklin, 1; Joseph, 55; Ann, 55; Rhody A. Crosthwait, 1; Willis Morris, 22. Joseph and Ann born in Virginia, all others in Ky.

1850 census of Lawrence Co., Alabama, district 8, enumerated 19 Nov, lists as household #483:
William Greenslade, 38, taylor, b. England; Elen, 25, b. Ala; Luke, 4, b. Ala; Ida, 2, b. Ala; Aaron Crosthwait, 27, farmer, b. Ala; Frances, 22, b. Ky; Catherine, 15, b. Ala; Elizabeth (Faucett ? Turnett? very ink smudged, may have been intentionally blotted out, begins with F or T and ends in tt, in between could be any three or four letters with no ascenders or descenders), 66, b. England.

It could be that Francis traveled from Kentucky to Alabama in between Sept and Nov, but what I think is more likely is that in September they were already both in Alabama, but their daughter Rhoda was back in Kentucky, being too young to travel safely, and the enumerator in Bath Co. was obeying the instructions to list everyone whose primary residence was in the household on June 1, 1850, and nobody else even if there at the time of the visit, while the enumerator in Lawrence Co., Alabama was not following instructions so literally. (My main reason for thinking this is Francis and Rhoda being listed in neighboring households in Bath Co. If they were both really resident there in Sept, mother and daughter would probably have been living together.)

Elllen and Catherine in this household are both Aaron’s sisters. One presumes that Aaron had travelled to visit them and introduce his bride.

1860 census of Rowan Co., Ky, Morehead P.O., enumerated 13 July, lists on p. 17 as family #122/126:
Aaron Crosswhite, 37, farmer, b. Alabama; Frances, 31; Rhoda A., 10; Turner, 4; Mary, 3; Louisa, 1. All except Aaron born in Ky.

1870 census of Rowan Co., Ky, Pearce precinct, enumerated 18 June, records on p. 125B as family #57:
Crosthwaite, Aaron, 45; Frances, 38; Turner, 14; Mary, 12; Louisa, 10; Aaron, 9; Martha, 5; William, 2; Kate, 6/12, born Jan. All born in Ky.

The next household is that of Owen and Mary [Donahue] Crosthwaite.

1880 census of Rowan Co., Ky, Pearce precinct, enumerated 1 June, lists on p. 29 as family #218/254:
Crosthwait, Aaron, 57, farmer, b. Ala Ky Ky; Frances, 50, wife, b. Ky Ky Ky; Louisa, dau, 20; Aaron, son, 19; Martha, dau, 15; William, son, 13; Kate, dau, 10; John, 8, son; Jacob, 4, son. All children born Ky Ala Ky.

1900 census of Rowan Co., Ky, Pearce precinct, enumerated 2 June, lists on p. 2B as family #34:
Crosthwait, Aaron Sr., 77, b. May 1823, Alabama Ky Ky, farmer; Francis R., wife, 70, b. Apr 1830, Ky Ky Ky, married 51 years, mother of 11 children, 9 living; Wm A., son, 31, b. May 1869, widowed, R.R. laborer; Jacob A., son, 24, b. Aug 1885, single, farm laborer; Blanch, granddau, 7, b. Oct 1892; John H., grandson, 4, b. Apr 1896; Mettie M., granddau, 2, b. Nov 1897; Daugherty, Myrtle, boarder, 18, b. Apr 1882, single, servant; Salyers, Shurklon (?), boarder, 20, b. April 1880, single, farm laborer. All except Aaron born Ky Ky Ky.

The next household is that of his son Aaron Jr., and the preceding one is that of his son John W.

The year of birth is almost certainly incorrect for William, since he was recorded as age 2 in 1870 and 13 in 1880. May 1869 would be only 8 months before the birth of Kate in Jan 1870, which would be extremely tight for a child who survived.