Arthur, William, Roy, and Kenneth are her sons, she died early of age so Robert Hay married her sister Isabel and she raised the boys and had her own children James, Myrtle and Velma 
Date: 12 Apr 1877
Place: Ottawa, Carleton Co., ONT
Notes: cert shows Robert as 21, b Russell, ONT, resid Wakefield PQ, blacksmith, Presby, s/o Wm HAY and Margaret MILLAR; Martha Jane 19 born/resid Wakefield PQ, d/o Wm FAIRBAIRN & Martha Jane ROGERS, Wit: Wm FAIRBAIRN Wakefield and Elizabeth STEWART Masham; 
Place: Wakefield, Quebec
Notes: FAIRBURN (sic): William 69 farmer; wife Jane 71 both b SCT; Willam 30 farmer b U.C.; wife Martha Jane 25 b Ireland; William 7, Mary Anne 5, Martha Jane 3, James 1 (born 1860), all b L.C.; Ellen 37 "wife of John Fairn b SCT; Frances 13, William 11, Jane 9 all b L.C. All Presb. F.C. Living in a "tide? log" building, 3 families, 1 hse being built 
It may be possible to confirm family relationships with Martha by comparing test results with other carriers of her mitochondrial DNA.
However, there are no known mtDNA test-takers in her direct maternal line.
It is likely that these autosomal DNA test-takers will share DNA with Martha:
I'll do it, but basically you note the WikiTree ID of Martha (Fairbairn-630) and go into William's profile to edit his mother, or note William's ID and add him as a child or Martha and Robert (then remove him from Isabella)