A big issue with Corrin is that she trusts people way too easily, despite the fact that she spent a good portion of her early life in isolation. She shouldn't trust the Nohrian royals because of the kidnapping, but on the other hand, she wouldn't feel any strong emotions towards the Hoshidans because although they are her siblings through blood, she doesn't have any strong emotional bonds with any of the Hoshidan royals, and thus no incentive to side with them. Throughout Birthright and Conquest, Corrin should show a distrust with either the Nohrian or Hoshidan royals, depending on the game. Distrust towards the Nohrians would be caused by the fact that they had been deceiving her her entire life, and the distrust towards the Hoshidans would be caused by the lack of emotional attachment.
Also, this is a little off-topic, but Corrin gaining the Yato should've been a bit more than "We found it in this thing that broke so it's yours now."