gazing from the shadows
They were laying the groundwork for that for a while. It was rushed at the end, as so much of this season has been. But burning the Tarleys seems to fit, and the building paranoia in the acting (reaction shots not just the lines) was pretty clear indication of what they had going on this season. It also fits well with the book based world building, the history of her house.The whole mad queen thing seems lazy...
Character wise, given past abuse (think of her brother and how he treated her for example) seeking power is a typical response, as is attacking those who thwart the seeking of power. She seemed to get less nice when her plans and views of her future were resisted or got derailed, even temporarily. I mean, she is super pissed her nephew doesn't want to bone anymore, as if that reaction is not a reasonable one. She is the center of her universe, and all must bend to that or face her wrath.
She seems to have become what her brother was, or would have been with the power of dragons at least.
I wonder how many children were named Daenerys, and what those parents think of the name now?