Francis, I have only second hand information, but it looks like you have it right that she is a daughter of John. But I have Mary and Catherine as two separate daughters: Catherine b. abt. 1841 in Hardy Township, Holmes Co., OH and died in 1930 in Holmes Co., married to George Fry, and Mary b. in 1844 in Hardy Township, Holmes Co., OH (See "The 1878 HISTORY of JASPER COUNTY, IOWA.")
Her ancestors were (parents) John GR + Mary Arnold, John GR + Susanna Brant, Albrecht + ??, Ulrich + ?? (immigrant of 1749).