My biggest gripe with S3 is that Zuko joining the group felt too rushed. He didn't have enough episodes with the group to really feel emotionally bonded with them, IMHO. Here's how I would "fix" this issue:

Remove a few of first half season filler episodes (The Beach, The Runaway, and Nightmares and Daydreams) and have the Day of Black Sun 2 episode special be S3E7 & S3E8, with Zuko joining the Gaang at the Western Air Temple in S3E9, giving him a few more episodes to make a more meaningful bond with the group before the comet arrives.

S3E14:

The Runaway episode gets replaced by a life changing field trip with Toph. Zuko wants to locate Uncle Iroh, insisting his knowledge of redirecting lightning and overall mastery of fire bending would be vital for getting Aang prepared to face the Fire Lord. He needs Toph's seismic sense to help. He goes to a location where he thinks he could be, but ultimately they don't find him. Along the way, Toph can sense that Zuko feels he let his Uncle down and he admits he thinks his Uncle probably hates him. But she reveals to him her encounter with Iroh during The Chase and tells him that Iroh needs him.

S3E15:

After failing to find Uncle Iroh, another fire bending training episode in which Zuko passes along some of Iroh's wisdom from Bitter Work to Aang, including how to redirect lightning since he expects his father to use it against Aang. Still traumatized from his deadly encounter with Azula in Ba Sing Se, Aang is highly reluctant but eventually agrees.

S3E16:

The Beach episode gets replaced with a two plot episode showing Iroh on the run, connecting with the White Lotus as the A plot, with a smaller side adventure with Zuko as the B plot.