This was confusing so I started at the beginning.
Absalom O. Ward
Married: 9 July 1829, Hempstead Co. AR
Source: Arkansas Compiled Marriages 1779-1850
1830 Hempstead, Arkansas Territory & Hempstead Co. Tax List
1840 Missouri, Hempstead, AR
1850 Bodcaw, Hempstead, AR
Absolom Wind, . KY, 44, farmer
Mary, b. Unknown, 33
James M., b. AR, 20, laborer
John W., b. AR, 18
Maniah, b. AR, 15
Mary A., b. AR, 13
David, b. AR, 8
Jessie, son, b. AR, 6
Thos J., b. AR, 4
Edward W. Beck, b. SC, 25, laborer
but no Sarah or William. Unless Sarah and William were born soon after Absolom and Polly/Mary's marriage, they didn't have those two children.
1860 Carouse, Hempstead, AR
Mary Ann Ward, b. AR, 48 living by herself
There was an A. B. Ward who married 1878 in Stephens Co. TX to a Mattie St. Clair but I didn't find Absolom or Mattie there. Successful Searching!