By the start of book two Ignis and Aeyron's relationship has be damaged, due to Aeyron's inability to control his grief. Ignis doesn't give up on Aeyron and does try to make things better for both of them, but Aeyron is always shutting out Ignis which is totally annoying him.
Ignis is trying to help rule the Seven Kingdoms but with the gap between him and Aeyron he's finding it exceedingly difficult, and even Aeyron doesn't come to him with things to do - he goes to Lord Tywon. So Ignis finds himself in a difficult position with Lord Tywon, who is also doing some of Ignis's job unofficially. Aeyron mistakes it and believes that Ignis is afraid of Tywon and not as cunning as him, and is being threatened which is why he's coming up to Aeyron and saying the things he is to him.
One problem with Aeyron and Ignis's relationship, is that Aeyron doesn't listen to Ignis anymore - like at all. He pretty much refuses to hear out Ignis, numerous times Ignis comes to ask about Ashara but Aeyron sends him away, ridiculing Ignis and shaming his family. Ignis feels guilt towards his sister that he can't do anything to will her aspirations into something material, and he also feels some resentment that Aeyron can go about ignoring him like that when he's supposed to be The Hand of the King. Aeyron can ignore Ignis, but not Tywon is his line of thinking.
Seeing as Aeyron doesn't talk to him, Ignis now organises in court - he makes moves to make useful allies like Loreon Casterly and Snakecharmer. Ignis may have connections in the city of King's Landing but he didn't need those connections in the Red Keep, everything has changed however and he can't trust people like Taena and Lord Ahriman. Ignis needs to get this hidden information that Aeyron and Tywon hide, and Loreon Casterly particularly becomes his partner. Loreon himself wants something in return from Ignis, which he keeps on repeating.
Ignis's family encourage Ignis to remove all emotion from his friendship with Aeyron and strictly look at it business-like, he's shamed Ashara and Arthur Swyft reckons that Ignis should let Aeyron know it straight how it is. Ignis's own wife, Jade, also encourages this line of thinking against Aeyron. She's encouraging Ignis to get away from King's Landing, and she tells Ignis the grievances she has with Aeyron and the toll Aeyron is having on her husband. Aeyron's actions and these people encourage Ignis to move away from Aeyron.
His family leaving King's Landing acts as a catalyst for Ignis to actually go ahead and start exploring things more. Jade tells him about the constant roaring in the castle and that he should check it out, Ignis remarks that Aeyron had told him it were ghosts and Jade tells him that you can't trust what Aeyron says nowadays, and he agrees. With the help of Jade, he goes looking after the roaring when before he had simply accepted it. Snakecharmer helps his quest and together thery discover that Lord Ahriman is responsible for it, and that Aeyron has solicited it. Slowly Ignis is uncovering Aeyron's secrets.
Ignis's arc is that he grows away from Aeyron, and just being his Hand of The King. Ignis is more than just the King's helper, he's his own man. Ignis doesn't make choices on how they'll affect Aeyron; he now makes choices on how it will better the kingdoms - even if it goes against the King.