I think blowing up a sept and missing (in all your delight about seeing hundreds of people die) that your son is going to be deeply depressed about it is kind of losing touch with reality. I'd say facing the prospect of either fighting an army of elite Eunuchs and Dragons united with the north or an overwhelming zombie apocalypse with no one but a mercenary company and a dodgy pirate by her side should make her desperate, but she isn't which to me is another sign of delusion.
It's true that from a modern point of view she faced adversity all her life, but at the same time, being a Lannister and being the queen she was always very powerful, giving her some measure of control over her situation and when she was young she could dream about being queen, when she was Robert's queen she could dream about getting him out of the way, when she was queen regent she could dream about creating a dynasty, etc. I think she's getting closer to the end of the line that regard.
Not that long ago she was completely outraged at the suggestion of being married to Loras, who being gay and a bit simple, would've probably been quite easy to manage/ignore. Now she's having to feck Euron (who shares a lot of bad qualities with her late husband) at his demand. That got to eat part of an already stressed soul and it signifies her loss of power.
Dany definitely has a strong feeling that being queen is her birthright and destiny and a certain harshness that comes with it, but on the other hand unlike Cersei she's also acted mercyfully and benevolent. She won't like Jon's claim, but I think it's pretty open what stance she will take after the inital shock.