How do think Dany will react if she finds out she's not the true heir to the targaryan dynasty?
Do you think she won't care and she's come too far or do you think she will yield the throne to jon?
I don't know why people keep saying this, Jon is
not the true heir to the Targaryen dynasty. Yes, he's the kid of the son of the last Targ king, but he's a bastard. Unless Aegon wrote a document legitimizing Jon right before his death (highly unlikely) Jon has far less of a claim to the throne than Dany.
She thinks she's way smarter than she actually is but she's no dummy. You don't get as far as she has if you're an idiot.
Nah, she got that far because she has plot armor/convenience on her side. Her actions in the season finale of Season 6 firmly put her in the "massive idiot" category.
Only an idiot would blow up the equivalent of the Vatican in a highly religious country like Westeros while you're in the middle of being investigated by the church (a fact that everyone knows). Not only that, by doing so she also kills the Pope, the Queen, her own son (indirectly, but if she was smart she would've seen this one coming) and let's not forget, almost the entire family of the ruling Queen. The same family who was providing the Crown money and the people food, because the Lannisters are flat broke.
Finally, as if she wasn't already the obvious culprit of this crime, she goes ahead and illegally declares herself Queen despite having no possible claim to that title (and to the people claiming Robert Baratheon did the same, he didn't, he had an actual claim to the throne, since he was the nephew of the ruling king).