With regard to her being "the Mad Empress," it's possible that this could be a case of perception over reality, if NRS was aiming to go really deep with the plotine (which I hope, they were, because that would be excellent story telling).
The perception would be in many ways earned, because for one, she actually was batshit insane for most of her existence, and even as she has found more rational footing in reality, she still engages in many tics commonly associated with the mentally ill, and still has trouble controlling her emotionial outbursts. Additionally, she's a cloned hybrid of two different species, and not necessarily a natural-born heir, and as such would be subject to lots of skepticism in a heredity monarchy based on lines of succession. For Game of Thrones Fans, it would be as if Tyrion Lannister was up next in the line of succession, but he was also a bastard with the unfavorable reputation of of a Stannis or a Cercei. The kingdom is ultimately going to depose you some way, regardless of how well you actually rule.
Ultimately it's possible she actually ruled surprisingly well, but ultimately had to climb too many hurdles for her rule to ever be respected or permanent.