The Hua Mulan & Commander Tung dynamic (and their relationship to Hua Zhou)
(I might be spoiling a couple of plot points from my fanfic canon rewrite in this post, so beware.)
Both of them wanted to emulate Hua Zhou in some manner - Mulan looking towards him in a superficial sense on how to survive in a man's world and in a war (via her Hua Jun persona), but also in a deeper sense trying to uphold the values and ideals that Mulan admired from her father (via the sword she had stolen from him).
On the other hand, Commander Tung thought very highly of his old friend and tried replicating Hua Zhou's legacy on the battlefield over the years since the day his friend was sent home early due to his injured leg, gaining status and respect in the military that would have probably belonged to Hua Zhou if he had stayed.
So when they first met and Commander Tung discovered Mulan/Hua Jun carrying around Hua Zhou's sword, they both developed a special kind of bond because the two reminded each other of Hua Zhou (the father/war veteran and the old friend/brilliant soldier), and for this very reason they understood each other in a way no one else could, not even their closest friends.
In Hua Jun, Commander Tung saw a young man, a little 'Hua Zhou' whose talents he quickly recognised and whose potential he wanted to cultivate. In Commander Tung, Mulan saw a father figure away from home, a second Hua Zhou who wasn't injured and was a badass and exalted general still serving his country in his old age. A living, breathing war hero.
Both of them talked praises of the other in front of their peers more than what seemed appropriate between a highly-esteemed general and his lowly subordinate, helping each other in a way more akin to a father caring for his 'son' and vice versa.
And yet, the balance of their dynamic depended heavily around their personal connection (past or present) to Hua Zhou, and it was ultimately held on by the thread that was Mulan's lie about her gender.
It was obvious that Commander Tung held more power in their dynamic, not just because he's much older and more experienced and he was Mulan's commanding officer and mentor. Mulan had much, much, much more to lose between the two of them.
Mulan had her own life at stake if her true identity was exposed, while Commander Tung at most would have his trust broken, his wish to see Hua Zhou again unfulfilled and his daughter unwedded. Mulan, being as young as she was, still looked for belonging, but Commander Tung already had all the prestige and status he could ask for as a war general.
As his own expectations of Hua Jun were shattered by Mulan's gender reveal (his friend Hua Zhou was never a girl in the first place), Commander Tung did one thing Hua Zhou would never do to his own daughter: cutting off Mulan's hair and disowning her from the army (her second home). And it almost broke her.
Then, something changed in their dynamic when Mulan decided to rescue the Emperor on her own (without Commander Tung's help).
That power begin to shift more in Mulan's favour, because she was right about the Rourans' plans to sneak into the Imperial Palace, she was the one who saved their country and Emperor in the end (for the second time after she saved the army from the Rourans with the avalanche). But more importantly, she had confidence in her own place in the world even if no one accepted her for who she was, and she had friends and allies who believed in her and would start a mutiny for her.
On Commander Tung's part, he began taking on more responsibility on Mulan's behalf. He realised that Hua Jun/Mulan's wellbeing (and the state of his country) mattered to him much more than his grievances towards Mulan or his personal debt towards Hua Zhou, so he tried making up for his mistake of not accepting her as a woman immediately by coming back around to support Mulan's mission of rescuing the Emperor and risking his life in doing so.
And finally, when the war was over, with Mulan hailed as a national hero in her own right and Commander Tung promoted to Grand Commandant, they both broke free from the expectations they had of themselves and each other.
Mulan/Hua Jun is not the Hua Zhou from Commander Tung's memories because she is Mulan. In the same vein, Commander Tung is not Mulan's father because Hua Zhou is her father. And that's okay. They reconciled and hugged and still care for one another and are proud of the other's achievements and see each other like a father and daughter.
And damn the movie for not giving us any of this delicious, juicy dynamic between Mulan and Commander Tung.
