I am still on this string.
The family story about Eunice being a daughter of Dull Knife is interesting. But Eunice was born in PA around 1820, and Dull Knife was born about 1810 in Montana. I am going by census records for the birthplace of Eunice.
Alfred and Eunice had an older son John Riley whose military records list him as being born in Bradford County PA.
As far as the correct spelling of the name it was Hemenway. All of the Hemenway's born in Bradford county PA at that time were descendants of Thaddeus Hemenway. The ones who moved to different areas changed the spelling to Hemingway or Hemmingway. I have no idea why.