There is a young, widowed Sarah Brereton, born Ireland, in Wakefield in 1871
https://www.familysearch.org/ark:/61903/1:1:KZG2-KFFThe two year son William, born Wakefield, this could be his birth reg
BRERETON, WILLIAM
Mother's Maiden Surname: TATTON
GRO Reference: 1868 D Quarter in WAKEFIELD UNION Volume 09C Page 31
Death of a Michael Brereton in Wakefield, March 1870, age 40.
Might be the husband.
Sarah may have later gone back to Ireland, where she met David? If so, there might not be any regimental link between the two men?