She went because she is the First Lady. She didn't wear a veil because she is an American woman and isn't submitting herself to the whim of Muslims. (including her husband)
I can understand your sentiment and in some ways I feel exactly the same.
However I don't think her behaviour was for the reasons you mentioned rather it was a diplomatic and protocol mistake made by the Obamas....which occurs only too often.
It was inevitable that the new King would snubbed Michelle , which of course happened.
Therefore why did the Obamas in their attempt at cringing affection towards the Saudis, make such a blunder?