I think Dany is certainly a bit mad. There are flashes of it, in both the books and the show. My guess in the books is that she'll have become more brutal when she returns from her little dragon side-quest (seems to have embraced 'fire and blood').     In the show, it certainly tries to portray her burning of the Tarlys as being somewhat unhinged.    She's not nearly as mad as her brother and father, but there's still something there.