I would be more accepting of Barry and Iris letting Nora stay in the past if the show were framing it as them wanting to spend as much time with her as possible because there's a real possibility they'll never get the chance to be a family again. As far as they are concerned, Barry still vanishes a couple years after Nora's birth. The problem is that they have barely touched on it after the premiere, when Barry was eager to send Nora to her time but changes his mind after he finds out he's not in her future. If this were a consistent theme, being willing to mess with the timeline to keep the family together, I would be more open to the bad decision they are making. It would still be selfish, wrong and dangerous but there would be a character-driven reason instead of the plot-driven mess they are trying to sell. As far as I am concerned, Nora is still in the past because JPK is a series regular and Nora is needed for the Reverse Flash plot.
Trusting Thawne? Wrong on so many levels. He's going to mess with them in the finale and they would only have themselves to blame. Thawne is such a master manipulator that he's IMO exploiting Nora's issues with Iris. I think he knew Iris would become such a pushover for her daughter, give him a chance because of her and be able to convince Barry as well.