It's family lore in my clan too. I've seen a photo of the person in question, and she looks Welsh to me; my grandfather is practically an archetype for ancient Welsh, despite being mostly English and Scots. She was a teacher in Michigan, so Cherokee seems an odd match if true; it might seem more likely if she were Chippewa or Sauk. But anyway despite the family lore making me too 1/32nd Cherokee, even if I could prove it I wouldn't use it for advancement. I've been discriminated against many times for being a Mormon, but never for being part Cherokee, which I told many people over the years up until I was old enough to learn it's probably not true.