How to explain the situation to Azula was indeed a headache. The main problem was not Yin Shu and Khen's romance, nor their child, Kii, but rather Yin Shu's choice to alter all her past memories.
Although Khen had also explained Yin Shu's struggles at the time, as well as her concern for Azula and Zuko, the outcome remained the same: she had ultimately chosen to abandon everything in her past.
Kahn could understand Yin Shu's decision.
She had been forced to come to an unfamiliar city and marry a stranger she did not like, forcibly cut off from all contact with her family back home, suppressing her longing for her loved ones and lover while having to endure her unwanted husband in every possible way.
What was more, that husband was a ruthless psychopath. Just thinking about it felt oppressive and painful.
That said, to Azula and Zuko, Yin Shu's actions were no different from choosing to abandon them.
How it felt to be willingly abandoned by their own mother needed no explanation.
Zuko might be able to understand Yin Shu, but with Azula, it was hard to say.
Azula had been deeply influenced by Ozai as a child. Yin Shu had always wanted to correct her, and had therefore been somewhat strict with her, which had also left Azula with certain prejudices against Yin Shu.
Although she had now escaped Ozai's control, some deeply rooted influences were not so easily erased. Coupled with her rather obsessive personality, Kahn worried that Azula would get stuck in a dead end again this time.
All the way back from Rah Town to the Imperial Capital, Kahn failed to come up with any particularly good solution, so he decided to rest for today and at least put it off until tomorrow.
However-