Entitlement is what Dany oozes through the novels. I deserve the iron throne, everyone else is evil for denying it, blah blah blah. I can't remember particular examples, I just found her personality to be irksome in this respect as I read. The Targs conquered Westeros less than 300 years ago, then they got conquered. Sorry your dad was a crazy piece of shit and lost the kingdom, but you aren't owed anything. Sure, you can fight to get it back, but it is no longer yours by right.
Well, she IS the rightful heir if Aegon isn't real and the ruling family from before the Aegon's Conquest happened has no objections, and she DID have her entire family killed because other people wanted to steal the throne from her and her family. She probably wouldn't care as much if she hadn't been hunted down HER ENTIRE LIFE and lost every family she ever had over it. Remember the first book? Drogo was not going to go across the sea to conquer Westeros, and she was okay with that. She was going to give birth to a son that probably would do that, but that was going to be on him. She was happy being the Khaleesi. Then Robert tried to kill her for having the gall to....have a child. She finally got a chance for a normal life and a new family, and here comes Robert trying to take all that away from her again. There is a lot more going on here than simple entitlement. For her, reestablishing Targaryen rule is the key to the safety and security of herself and her people.
And it also makes no sense that you promote Aegon if that is why you had a problem with Dany? He too had his life fucked over, but Dany was willing to let the matter go until the assassination attempt. Aegon, by all appearances, always fully planned on retaking the iron throne for himself even if Robert never attacked him. He is far more entitled than Dany.
She is an incompetent ruler who rejects good advice when it's given. She is an incompetent raiser of dragons. That is admittedly not her fault, there isn't that much expert advice on how to raise a dragon. Sure, it is good that she didn't let them run around and kill people, so it is good that she tried to remove the threat. Not unlike a WMD in a silo, neh? But even that plan was shit. She had feral dragons probably not long from breaking out and wreaking havoc. She took no affirmative action to figure out what the fuck to do about them. And it all went to shit.
I'm not saying she didn't HAVE WMD's, but she didn't use them irresponsibly like your implying. What do you suggest that she do if not lock them up somewhere? How do you teach a dragon "No, don't eat that child"? Especially now that they are big enough to be ridden. It's not like a dog where you can pull on the chain or something when it's about to do a bad action. They don't have electric collars and if they try to do anything at all, the dragon is more likely to fry them alive than back down. So how was she suppose to come up with any other solution besides "Lock them up so they don't do more damage."
Also, keep in mind that Dragons really aren't much good for anything but destruction and wreaking havok. Remember that she was trying to run a city peacefully. Even if we assume she could have got them under her complete control, what was she suppose to do with them? Her the main problems were nightly assassinations, diplomacy conflicts, hunger, and disease. How would dragons help with those?
I never had a problem with her until Dance. Before that she was a fine character, some boring stuff, but some particular highlights. Dance exacerbated the bad and lacked a redeeming moment.
The main problem with her chapters is that they take place in an area we don't have as much investment in and that she is incompetant at what she is doing. The names of the people were strange and foreign. If the exact same events had transpired in Red Keep, we would have not been as disconnected by simple virtue of familiar faces. The fact that Dany is incompetent at what she is doing doesn't help either, because it's always more fun to read about a character who is consistantly awesome. But one of the strengths of ASoIaF is that it is realistic. And there would have been nothing realistic about Dany being awesome here.
However, it's not like her situation was as simple as most haters would like to see it. Like I said about the infected people outside her gates, both solutions had their strengths and weaknesses. Part of Dany's problem is that she is too empathetic for politics. All she has ever wanted to do since ACoK is help her people, so when she sees them suffering outside, the smart decision would be to leave them alone, but also a very cold one. And Dany is not cold to her people. So if she had done that without a thought, it'd have been out of character and perhaps made her far less likable for being so callous.
On top of that, she always had to deal with A LOT OF SHIT that most normal people would have cracked under. Who was on her side? Who was plotting against her? She needs to make her city prosper, but to do that she needs to cut off other helpless people that she personally promised to save. But if she does that, how can she be any different from the other tyrants in the city. She is suppose to be a savior to these people, isn't she? But how does she help? Is taking away the fighting pits TRULY the right thing when it's such a part of their culture and the fighters themselves want it so badly? And what about her own personal happiness? She has to marry a guy she finds repulsive in almost every way and he could be a harpy on top of that so that the city she promised to save prospers.
Get over the distaste of Dany not being awesome at everything she tries (thus, preventing her from being the mary sue that people have called her up until this book), learn to deal with the foreign names and stuff, and you can find a pretty compelling arc that explores a new side of Dany's character and what it means to rule.