We tend to see Iroh through Zuko's eyes, so it's not surprising that most fans share Zuko's perception of his uncle (to the point where plenty of people, including the creators, often refer to the character as "Uncle"). His reputation tends to be one of a warm, generous, compassionate, peace-loving, understanding old man. And he certainly earns all of those adjectives over the course of the show. But it would be a mistake to assume he was born that way, and I think the show indicates that he was not.
To be sure, Iroh is always depicted as mentally healthier and less violent than the rest of the Fire Nation royal family. He refuses to kill the last surviving dragons, and he shows elements of his fuddy-duddy persona when writing to his niece and nephew even when presiding over the siege at Ba Sing Se. But let's not forget what he was doing at that siege the rest of the time. Iroh was a successful general; even Zhao respected him for that. He dreamed of being a conqueror and spent almost two years leading what had to have been one of the largest campaigns in the entire Hundred Year War. While he might not have fully embraced the ultra-nationalist ideology, Iroh was still an active participant in Fire Nation imperialism.
The turning point, of course, was the death of his son, Lu Ten. Iroh called off the siege to grieve at home, which disgraced him in the eyes of Fire Nation militarists and probably contributed to the ease with which Ozai pulled off his coup. Once he returned, Iroh took Zuko under his wing (especially since Zuko's mother had just disappeared). Now this is where Satch made the interesting point that Iroh seems to have basically written off Azula. I don't agree with Satch's complaint that Iroh seems to have disregarded Azula's hopes and dreams by sending her a doll as a gift; he hadn't seen her in two years and probably didn't know either his niece or his nephew all that well. But after his return, he sees in Zuko another lost and grieving soul, and one whom he is able to help, and thus to maybe atone in part for his failure as a father. (This is where I have to point to the fan theory that Lu Ten committed suicide >
link<, which is entirely speculative but IMO quite convincing.) While I'm sure Iroh cared for Zuko, I think he was reaching out as much for his own well-being as for Zuko's. We don't know if he tried to reach out to Azula too, but even if he did, she made no secret of her disdain for her "failure" of an uncle (already being daddy's little imperialist).
In any event, Iroh seems to have renounced all ambition and most of the trappings of his former life by the time the show starts. He knows that Zuko's pursuit of the Avatar is a fool's errand, and treats the voyage as more of a vacation during retirement than anything else. We know that he's concerned for Zuko's well-being, and tries to watch out for him, but at the time of the pilot he doesn't think the Avatar is a factor so he lets Zuko pursue potential leads with only gentle rebukes and cautionary advice. Even during the season 1 finale, Iroh didn't try to stop Zuko from going after the Avatar, and he doesn't explicitly call Zuko out until almost the end of season 2.
But what would be going through Iroh's mind when he realizes that the Avatar is in fact alive? He doesn't seem to show much surprise or even interest when he first sees Aang on the ship (not having personally witnessed him airbending against Zuko), but once he sees Aang flying and wrecking shit for himself, Iroh is clearly taken aback. Does he work with Zuko in attacking the avatar because, in a moment of shock, he simply reverted to old habits? Perhaps he had not ever considered the possibility that the Avatar would show up (I think this is likely), so he had not planned what to do if he found himself in a fight. I'm not sure Iroh would have let Zuko take Aang to the Fire Lord without trying to dissuade him along the way, but he would've had time to come up with a strategy if Aang hadn't escaped so quickly. As impressive as that fire blast looked, it wouldn't have been fatal; not the way firebending works in ATLA.
I know I'm just speculating, but your post really got me thinking. There's a very good chance that you're right and it is just early installment weirdness, but I prefer to try to come up with in-universe explanations first if at all possible. However, I do have to admit that I'm not sure how to square Iroh's backstory with his documented involvement in the Order of the White Lotus. Why would a general in a conquering army be part of the White Lotus of ATLA (which shares almost nothing except the name and logo with the organization from TLOK), an internationalist and largely pacifist organization? The best solution I can come up with is that Iroh did not join until after Lu Ten's death, but I can't recall if this is supported or contradicted by anything specific in the show.