I would say that the children were all born in Crawford Co IN, Isiah din't show up
in Greene Co Ar till after 1870 census.
My mother also told me Isiah had brothers James, Henry and Frank

I do see James here maybe the others are who they went by

Husband: William Mitchell
   Born: Abt 1794       at: SC  
Married:                  at:   
   Died: 19 Oct 1879      at: Crawford Co. IN ,Newton Cole Jones Cemetery
 Father:  
 Mother:  
        Other Spouses: 
   Wife: Elizabeth King
   Born: 1799             at:   KY
   Died: 1871             at: Crawford Co. IN,  Newton Cole Jones Cemstery
 Father: 
 Mother: 
        Other Spouses: 
CHILDREN
   Name:  Isaac Mitchell Sr.
   Born: 26 SEPt 1820     at: KY  
Married: 12 Oct 1843     at: Crawford Co. IN. <>2 Oct 1859 Crawford Co. IN   
   Died: 2 April 1892       at:  Crawford Co. IN, Bethany Union Cemetery
Spouses: 
   Name:  Ferbia Pheby Mitchell
   Born: ABT. 1822        at: KY  
Married:                        at:   
   Died: 10 April 1908    at: Binger Ok.
Spouses: 
   Name: Sarah Mitchell
   Born: ABT. 1826        at: Crawford Co. IN
Married: 22 June 1852   at:  Crawford Co. IN. 
   Died:                  at:   
Spouses: 
   Name:  James Mitchell
   Born: ABT. 1827        at:  Crawford Co. IN.  
Married: 29 Jan 1846  at:   Crawford Co. IN
   Died:                  at: Mitchell Cemetery, Crawford Co. IN.
Spouses: 
   Name:  Elizabeth Mitchell
   Born:  ABT. 1831       at: IN  
Married: 10 June 1852  at:   Crawford Co. IN.
   Died:                  at: 
Spouses: 
   Name: Dicy Mitchell
   Born: 1833/1834        at: IN
Married: 22 Aug 184     at:   
   Died: 1857                 at: Newton Cole Jones Cemetery, Crawford Co. IN  
Spouses: 
   Name:   Isiah (Bud) Mitchell Sr.
   Born: 1834             at:  IN 
Married:                  at:   
   Died:                  at: Mt Home Cemetery, Greene Co. Ar
Spouses:  Sarah Trusty
   Name:  Pharyabe Mitchell
   Born:                  at: IN ?  
Married:                  at:   
   Died:                  at: 
Spouses: 
   Name: William Mitchell , Jr.
   Born:                  at: IN ?
Married:                  at:   
   Died:                  at:   
Spouses: