1) Its quite possible though, her dragons are the only ones in history that can't be directly controlled by their Targaryen master. As much as you want to blame her for this, she wasn't trained. 2) Not only no Targaryen who knew the techniques was alive to teach her, the dragons were thought to be extinct.
At this point, 3) two houses have relevance and power. Tyrells and Martells. Starks and Lannisters are exhausted. 4) Martells are guaranteed to support Dany and Tyrells might or might not. But given that they owe everything to Targaryens they are more likely to support her than Stannis.
That's not true. Dragons aren't 'controlled'. They can be tamed, and they can listen and obey instructions of their riders, but at the end of the day, they are still wild beasts. They can't truly be broken or controlled. As well, your post implies that the Targaryens are the only dragonlords in history. If you don't know the lore, don't make proclamations about it. The Targaryens are the last vestige of the Valyrian Dragonlords, and they weren't even close to being among the most powerful of families.
There's no technique for it: She's their 'mother' who birthed them. They recognize her as someone who is a maternal figure to them.
You're forgetting a great deal of houses throughout the Kingdom, most notably, House Arryn, and the Vale. The Lannisters are also still in control of the Iron Throne as well. The Starks still have a potential powerbase out of the North and the Riverlands, who mostly are still loyal to the Stark memory.
The Martells are not guaranteed of anything. In the books, at this point, they're even less likely to support Daenerys after she rebuffed their offer through Quentyn Martell. They're much for likely to support fAegon!, especially if he turns out to be their long-lost relative.