This scene was what always confirmed to me that Ozai cared about Ursa. He obviously couldnβt tell Zuko why she had gone - it would amount to telling him that he had gotten the throne through treason, and children are hardly the best secret-keepers. So he keeps silent, sacrificing the chance for Zuko to get closure for the sake of maintaining the lie Ursa helped him craft.
Yet he lingers contemplatively by the spot she had recently occupied and stares at the fountain that wonβt play anymore. That doesnβt scream βheartless husband whoβs having a blast now that his annoying wife who could poison him is goneβ. I wouldnβt even pin it on relief, which heβd probably be feeling in the comicsβ version after eliminating a serious threat to himself. The whole mood here points to Ozai being contemplative about her departure.
It could be that he loved her deeply and was mourning the loss. Or maybe he hadnβt even realized that he cared for Ursa up until this moment, when he realized sheβd never sit in that spot again.
Wherever their relations fall on the Urzai spectrum, his mood here is clearly one of gravity. He wasnβt unaffected by Ursaβs departure. What more, Zuko is able to intuit that somethingβs wrong without Ozai having to say a single word.
This is an interesting moment of communication between Ozai and Zuko. In normal situations, Zuko is probably used to Ozai always having something to retort with - especially if itβs talking to him. Really, it wouldnβt have been out-of-character for the confrontation to have taken place somewhere in the palace, with Ozai looking all regal as the new Fire Lord and curtly telling Zuko that Ursaβs whereabouts were none of his concern.
But Ozaiβs out by the fountain, and he says absolutely nothing. This isnβt typical Ozai, and Zuko knows it. Whatever emotion Ozai is displaying (we canβt see his face, but presumably Zuko can), Zuko knows that only something serious can make his father react this way. So whatever happened to Ursa canβt have been good.
Itβs also interesting how Ozai takes Ursaβs place by the fountain at the same time as he figuratively takes her place as Zuko and Azulaβs chief caretaker. This is illustrated nicely by how Zuko is the one to rush out towards the fountain, where Ursa was often seen, and find his father there instead. Where a mother once was now stands a father, and Zukoβs not sure if heβs happy about it.
Thatβs why I also see this moment as the moment where Ozai resolves to take the reins and assume sole responsibility for Zuko and Azula. Just like they would have to accept without explanation that their mother was gone, they would have to accept the new life Ursaβs sacrifice had given them.
In light of this, I like to think that Ozai did place an importance on being a parent towards his children. But he also wanted to make sure they were raised his way from now on - the way a Fire Lordβs children should be raised. He wasnβt just dragging them along like unwanted luggage, or even plotting to use them as tools. Not yet, at least. In the wake of Ursaβs absence, he stepped up to the task with awareness and determination: he wouldnβt be soft like she was, but he would mold Zuko and Azula to something befit of the title βprinceβ and βprincessβ.
Unfortunately, these good intentions paved the road to hell.