Its not so much a case of Hime Kinu hating your or not caring about you, but rather this was a young foxling who had to grow up without her sire for over a decade and became attached to the only parent that could still be around. She takes after Kiyoko because Kiyoko became the biggest influence in her life, and she took those lessons from her mother more readily than what she could have learned from her sire. She's learned to walk the walk, talk the talk and stopped wearing her heart on her sleeve. Especially when you consider the sheer amount of pressure Hime Kinu is under; being the firstborn, she's running the house, expected to be perfect and expected to one day become a denmother herself. That's a lot to hide behind a mask of indifference.
Contrast that with the Inari version of Kinu, you have a young woman who is more down to earth, but who perhaps happier with herself. This is a young woman who prefers the company of crops than other people, but she's much more her sire's daughter. She's energetic, bubbly and far smarter than many people give her credit for. She's also far warmer to the Champion than Hime, and certainly has a better relationship with them then she does with Kiyoko.
Its almost as if your actions towards your child when they're growing up has an impact on them as an adult.
I'd argue it's not quite that, even. Really, it's largely reflected in the shorthand used to describe them: "Kitsune
Hime" and "Inari
Shoujo". Literally Princess and Girl, respectively. They're fundamentally the same person but it's down to attitude about their role and their outward expression in support of that attitude.
Hime is a princess first and foremost and tries to act in a way befitting that role. Being your little girl takes a backseat to living up to the ideal of that role. As the saying goes "heavy weighs the crown", and Hime is acutely aware of the implicit and explicit duties and expectations of her station, especially considering her recognized brilliance and the symbolic weight of her white fur.
Based on what we know of the culture, the combination of her fur and her heritage means it's highly probable that had she been born in her ancestral homeland she would have been arranged to be married to someone in the ruling family itself. Here in the colonies, that's not an option - especially considering the political landmines that came from Kiyoko's two century absence - but expectations for her are still sky-high and nobody makes a secret of that. Hime is the daughter who tries to be an exemplar, a perfectionistic lead-by-example type who religiously stands on ceremony because she's terrified of being caught without her makeup on, so to speak. She puts a huge premium on the idea of earning and validating the expectations that she's under, and treats any lapse in her abilities or decorum as a failure. Think back to when she got sick over her difficulties in learning the bow and naginata. Hime is the version that says "I know I can be better than I was then".
"Inari" ("Shoujo", really), is the flip side of the coin. She's your little girl first and a princess a
distant second. While Hime does her best to model herself off of her people's expectations, Shoujo seems indifferent to them if not outright disdaining them.
If I were to sum each up in a word, it would be "overachiever" and "underachiever". Hime and Shoujo are two reactions to the expectations put upon a genius. Hime is the genius overachiever, who reasons that as a genius who is capable of more than most, it's her duty to surpass everyone's expectations. Shoujo is the genius underachiever who reasons that putting people like her on a pedestal is unreasonable and as such she's not going to bother trying to live up to such expectations in hopes that they'll eventually stop expecting her to do something special. Returning to the bow and naginata, Shoujo is the version that says "why should I make myself sick trying to live up to others' expectations?"
However, I think the moment that
really highlights this contrast is when you compare Kiyoko's opinion to the variant Kinu's fiancees. With Nakano, she likes the match specifically because he's ambitious and wants to accomplish great things. Therefore Kiyoko reasons that he is a partner that would help Kinu's brilliance shine all the brighter. Conversely, she doesn't like the match with Hitoshi specifically because he's complacent and has no ambition beyond tilling the fields and coming home to a happy family, which she sees as something that will drag Kinu down and give her no outlet for her talents. To use contemporary parlance, there's more than a little resonance with the wry "she went to college to get her Mrs." quip.
It's an external perspective from Kiyoko, but I think it hits at the heart of the key difference between the two Kinu variations, as reflected in their fiancees. One feels obligated to push herself past the point of reason until she does something world changing or breaks, the other is complacent and satisfied to squander her abilities in a simple unchallenging life. Both are flawed perspectives that need to be curbed, but they're the flip side of the same coin, divergent personas rooted in how Kinu has come to view
herself and her role.
Back to my original point, these attitudes inform the persona they adopt, which influences them both publicly and privately. Hime embraces her princess role and therefore utilizes a much more formal persona, taking special care not to make the smallest misstep and trying to live up to a romanticized ideal of how nobles and royalty
should act (tangentially, this is reflected in how Hime was also the 'encourage romantic outlook' route, and Kiyoko notes that she probably let the girl read too many romances when she was young). Hime consistently puts on a brave face and tries to be what the people around her expect her to be.
Conversely, Shoujo instead opts to reject that with a much more casual country girl persona. Whereas Hime goes out of her way to conform to people's expectations, Shoujo is stubbornly willful and individualistic to the point of being dismissive as a matter of principle. She doesn't care what everyone else thinks, she's doing it her way, and that's that.
This probably goes a long way to explaining the perception that Shoujo has more affection for her sire: She's
casual. There's a very simple dialogue tweak that arguably encapsulates this damn near perfectly: Hime calls you "Father", while Shoujo calls you "Dad". That's very much a reflection of formality, but we're also kinda conditioned to see the former term as cold and distant and the latter as warm and familiar. It's not necessarily the case - and I'd argue it isn't the case here - but experience within our own modern cultures prejudice us to that conclusion despite it contextually reflecting a broader pattern in their attitudes and speech. Hime stands on ceremony in a way that Shoujo does not.