I am not quite sure if she was really mad and in which degree. It is known to me that she had outbursts of rage during her pregnancies and tyrannized her servants during both pregnancies (she had two sons). From other sources I get the impression that she was highly sensible and very homesick to her mother. In her early wedding years she visited her homeland and than started crying (as I remeber reading in a book about her mother Marie Louise of Hessen Kassel) as soon as she saw the church tower of Arnhem (she must have travelled by boat down on the Rhine to the Netherlands). So she certainly was a emotional personal.
I am sure her mother raises her to be a good and kind person, so to speak as Marie Louise was herself. Maybe she could have been treatened very easily (by our standards today) for her mental illness, allthough it is not clear to me what she was suffering from.
So alltogether I would say that it will not be easy to find a good portrait of her. Maybe this summer I will visit karlsruhe and Baden Baden. Perhaps there is more to be found overthere.