You should go back and reread ADwD because those issues are address or attempted to. I get that you don't like Dany but your judgement about her is heavily clouded. It is unlikely Dany expects everyone to like her since up-until her relationship with Khal Drogo, her main human relationship (her brother) was abusive. 14+ years of abuse will do that to you. Moreover, given the situations she has overcome she isn't weak. I will not say she doesn't have flaws, she does. Many of them due to her young age: she's self-righteous, prideful, quick to anger, naive/innocent, among other things. Weak? No. Maybe a little crazy, but not weak. A weak person could not do half the stuff she did.
Also, all her knowledge of her family up-until recently in the series came from her brother, Viserys. Who, as I recall, didn't spend much time with his father. Moreover, I think he was completely removed from the Red Keep towards the end of Aerys the Mad's reign. He didn't get to see his father's fall and as a kid was most definitely kept out of the loop. So yes, Dany was obviously bias about her dad because the only source of information was her brother. It is only later, in her encounters with (SPOILER)Selmy Barristan that she gets a much better understanding of the cruelty of her father.
Mostly, it seems like you are projecting Viserys' flaws onto Dany which is severely unfair. Given if you take their leadership and ability to move people to their cause, you can see the Viserys serves more as a foil for the type of ruler Dany is becoming. She may not be the cleverest girl, but she isn't stupid. She saw what her brother's behaviour got him. I am not saying that she isn't without flaws; the books do acknowledge that through other characters. But it is not the picture you are painting.
As for people whispering about the return of the Taragryen to Westeros? It is fair to put some of that on Viserys' conceit. Yet, at the same time it is basically what it appears that (SPOILER)Varys is planning by pushing Westeros in ruins and setting it up to be saved by a Targaryen (assuming that is his plan and not just another front of his).