First thing we should note: in all answer choices, the first chunk of the sentence (in A: "In 1945, after a career as First Lady in which she shattered expectations more audaciously than either Abigail Adams or Dolly Madison ever had been,") is a modifier that should describe a first Lady: Eleanor Roosevelt. Modifiers should always be placed as close as possible to the word they are describing so we know that it is what is being described. In A, D, and E, the closest noun is "Eleanor Roosevelt", so that works. However, in B and C, the closest noun is "President Harry S. Truman". He was never a First Lady, so this doesn't work at all. Eliminate B and C.

Next thing we should note: in A, we see the phrasing "more _____ than". This means we have a comparison. When we compare two things, those things MUST be parallel.

A. she shattered expectations more audaciously than either Abigail Adams or Dolly Madison ever had been

Here, we want to compare how "she" (Eleanor Roosevelt) shattered expectations to how Abigail Adams and Dolly Madison "had" (shattered expectations). Adding the word "been" messes up that parallelism and confuses the meaning - what had they been doing? Eliminate.

Now we're between D and E.

D. with an audacity never matched by Abigail Adams or Dolly Madison, Eleanor Roosevelt was appointed a delegate to the United Nations General Assembly by President Harry S Truman

E. with an audacity never matched either in the case of Abigail Adams or of Dolly Madison's, Eleanor Roosevelt was appointed to be a delegate to the United Nations General Assembly by President Harry S Truman

We should notice right away that E is less concise, so we should already not like it. We should then note that some of the phrasings that make E longer are less idiomatic than the ones in D: something is matched "by" something, not "in the case of" something; people are "appointed delegates", not "appointed to be delegates". So we can eliminate E and pick D.