Grandfather has claimed Cherokee blood in the family – but is there?

My grandfather has always claimed that there was Cherokee blood in the family. My Uncle before me, then myself have not found it listed anywhere. The family line is VERY English (Yeomans) – but there is a ton of family drama and research has shown me something new. My grandfather’s mother did not die, she left my great-grandfather and remarried. I found a picture of her daughter with that second husband, and she is NOT very English. My great grandfather did not keep children born of one marriage when he remarried, so my grandfather must have gone with his mother in the divorce, and he finished growing up with his mother’s second husband and his half sister and half brother. How do I find out if husband #2 and the children were of Native bloodlines? Great Grandmother’s name was Emma Eveline Smith (1868ish – 1903 – Michigan), her second husband was John A Payne (b: 5/22/1855 – Tompkins Co NY ; d: 6/17/1911 – Edmore MI), my grandfather’s half sister was Maude T Payne (b: 11/29/1891- Alogma MI; d: 10/12/1940 – Mecosta MI). All records I have found to date say that everyone is white, but looking at Maude’s picture, she is not white. Is there truth in my grandfather’s life long story? Or not?