I think people are thinking about this just a little too hard. Just a little.
If you'll remember, Artoriel was originally very headstrong and stubborn and insisted he didn't need our help. He actually admits that some part of him wanted us to fail and die on our co-op mission out in the Western Highlands because Haurchefant praised us so highly. Our success and conduct won him over during the mission, though, and he pledged not to doubt us again. He had a very professional demeanor, even if he was rather rude to us at first.
Emmanellain, on the other hand, was portrayed as a carefree fool. He is much kinder than Artoriel even in the beginning, but treats the mission like a game. After arriving at Camp Cloudtop and flirting with Lady Lainette, he's assigned surveillance - an unglamorous but necessary task - and he ends up getting captured by the Vundu. We go to rescue him, and he cowers behind us every step of the way during the escape. Once we return to the manor, he expects to be praised for his efforts and conduct, but ends up (rightfully) being scolded.
That's all we really saw of the two before 3.1.
As for Count Edmont, the Quest Log does indeed say that he regards Aymeric as a son. That said, at the present time it's rather understandable - he and Haurchefant are a lot alike in many ways. Aymeric has also been put into the position of being Ishgard's icon of hope, willingly or otherwise, and losing him would at present throw the nation into chaos. We also later learn that Edmont is going to step down as head of House Fortemps, so I'm willing to bet he was trying to impart some last wisdom to the young Lord Commander before he does so.
From all of this, what I can gather is...
Artoriel is hesitant of the change in Ishgard, but also accepting of the truth and willing to take up the burden of being Count so long as he has someone he can rely on to support him. He is afraid, but he's not going to let his fear stop him from doing what he believes is right for Ishgard. Many of the things he does here seem to be to prove to himself that, even if the title of Count is built on a lie, he has earned it. He doesn't want it to just be handed to him, and in the scenes with Count Edmont seems to be trying to gauge what exactly Edmont is trying to do.
Emmanellain, on the other hand, is probably not taking the change well. Compared to the other members of House Fortemps, he's rather cowardly - just a braggart, really. Honoroit also mentions usually having to comb the taverns to find him, so he's probably quite the drinker on top of it. I'd wager he's just trying to come to terms with everything, and isn't doing so quite as well as Artoriel. Having more responsibility put on him probably isn't going to end well unless it's done slowly as Edmont suggests. I think he is angry due to a number of factors, from Edmont being so close to Haurchefant despite the latter being a bastard child, to the endless praise he has for the Warrior of Light, to the regard he holds Aymeric in, to jealousy over Artoriel finding his conviction. Emmanellain seems confused and unsure of what to do or where he fits in, something I am all too familiar with.
That said, I don't think there's anything particularly bad brewing in House Fortemps. It's just a microcosm of the political strife within Ishgard if you ask me.