While this doesn't give the information you were looking for about Nina's parents, it's an interesting bit about her - provided that the Mrs S S from the obituary Margaret found is the same as Mrs S A, which name the following volume uses:
Garfield County, Oklahoma, 1907-1982, Volume 2, pages 837, 838, published by the Garfield County Historical Society:
excerpts: "HUNTER . . . The old newspaper listed the charter members of the Christian church . . . Mrs S A Riggs, E M Riggs, A A Riggs, Pearl Riggs, . . ."
"HUNTER CHRISTIAN CHURCH Largely through the efforts of E M Riggs, [and other listed]. . . enough subscriptions were secured to build a church . . .
J H Robinson was overseer and main carpenter, E M Riggs . . . Steve Riggs . . . and other assisted in the work.
The Hunter Unit of the Oklahoma Missionary Society was organized in the spring of 1918, at a meeting held in the home of Mrs Steve Riggs."
You might send for a death certificate for Nina; there probably would have been one by 1925.
Also check the Garfield County GenWeb page for a link to Enid funeral homes to contact them to determine who handled the arrangments for Jane, Minnie and Nina.