The answer is Edwina McDonough. Frances McDormand did not portray Edwina McDonough in a Coen Brothers film. However, she did play the roles of Abby in "Raising Arizona", Marge Gunderson in "Fargo", Doris Crane in "The Man Who Wasn't There", and Linda Litzke in "Burn After Reading."
Uncovering the Remarkable Journey of Frances McDormand: A Quiz on the Acclaimed American Actress