People often talk about Dany locking up Rheagal and Viserion under Meereen is a proof of how good she was.
I was -extremely- mad at her for that decision, and thinking back on it now, it's even more obvious that this was never a good decision. It was pure Dany, doing the wrong thing, for good intentions. She punished two dragons who had done nothing (and were described in the books as being the nicest dragons) for what Drogon had done (while he was never punished for it). This is never a good way to teach animals, not even dogs, and if they are indeed really intelligent, it's even crueler.
It's really a trend for Dany at this point, that she generalizes very quickly. One dragon does something bad, all dragons are guilty. Lots of Masters do bad things (crucifying children), all of the Masters are guilty. Something doesn't align with her vision of what's good? Ban all these traditions immediately, alienating people in the process, instead of slowly teaching people how to change their ways. It's actually a common theme in our world today. People think the only way to do something good is to destroy practices that are not considered to be good overnight, instead of teaching people how to change, which takes years and years, sometimes generations.
Even though I did support Dany for her ideals, I did see how she failed sometimes (probably still missed some), and when she failed, it was always with a high cost for everyone else. That, and you don't send your children to fight for you, you try to protect them instead, unless you see them as little more than war assets, which is disgusting.
So I think her going this way is actually fantastic, even though I do admit that I'm not all on board with how it was done in the show.
Now concerning how the story is told in the books, I really hope that she will not get Rheagal and Viserion's trust right back when they get free. I really hope she will have to work for it, because in the show, they started helping her immediately, and that felt really cheap to me. Or maybe that master she fed them was really super tasty or something.