I don't have access to online 1930 census for OK at home.
But, since you say her parents are born IL, here is someone to check out.
1900 census Delta Co, TX:
Kenady, Charles A., h, b Dec 1843, M 13 yrs, b IL, IRE, TN
" Texia, w, b Apr 1873, 27, M 13 yrs, no ch listed, b TX, KY, KY
Pennington, Melinda, mth-in-law, b Oct 1836, 63, wid, b KY, KY, KY
" Dora E., niece, b Nov 1887, 12, b TX, TX, TN
Looks like Charles has a second younger wife, but I'm willing to bet there is some kind of connection to your gal and her family.
1920 census Pushmataha Co, OK:
Cannedy, Bennet[sic], h, 2?, md, b TX, IL, TX
" Ethel, w, 29, md, b MS, MS, MS
" Anna Lee, d, 14, b ?
" Clifton, s, 9, b OK
" Oscar, s, 7, b OK
" Kenneth, s, 1 11/12, b OK
" Berthem, s, 1/12, b OK
[note, Bennet's mother born TX, you said Cloy's was IL, maybe he is a half brother, as you said]
Happy Hunting (^_^)