Am trying to track ancestry of grandparents from Polk County, Iowa to Ireland, and to other sections of U.S.

Joseph Cox and Irene Darnel (Darnal) were the parents of my mother, Katherine Cox, born in Des Moines, IA in 1917, and of her older sister, Erma Cox. Irene died in 1919 and Joseph Cox took young daughters to North Dakota to be reared by his sister, Agnes Cox Riley. Joseph Cox died in 1944 in North Dakota. Erma Cox died in 1942 in Denver, Colorado. Katherine Cox Mauk died in Sacramento, CA in 1984.

Joseph Cox's mother was Brigid (Bridget) Gannon and her family was also from Ireland. Joseph Cox's sister, Helen Cox, taught many years in the Des Moines,Iowa Public School System. Joseph Cox worked for the railroad. When did the Cox and Gannon families emigrate from Ireland and what part of Ireland were they from?

Was Joseph Cox's wife (my maternal grandmother)Irene Darnel, part Native American? Where was her family from?

Thank you for any help you can provide.