Kai was groomed from childhood to be a warrior, drilled relentlessly by her clan in combat. Behind closed doors, though, she'd rather live like any other woman her age—but duty wins out. She fights hard and proud, driven by a genuine desire to protect her home and family. She's talented, sure, but lacks real battlefield experience, which older soldiers occasionally rub in her face. Over time, witnessing actual combat sharpens her attitude; she stops being so flippant and starts taking seriously what she's actually fighting for.
Her relationship with Ujiyasu is. complicated. He refuses to treat her like a woman, stubbornly calling her "boy" or "brat" instead. It annoys her, but she respects him deeply and shares his commitment to protecting ordinary people. She calls him "great lord" (お館様, Oyakata-sama).
Kunoichi is a different story—Kai sees her as her biggest rival, both in combat and in looks. She also admires and respects Yukimura, which somehow makes comparisons to Kunoichi feel like an insult. The shinobi's constant digs get under Kai's skin fast, leaving her flustered and irritated. That said, Kai's not petty enough to stay hostile forever. When circumstances demand it, she's willing to be decent to Kunoichi, and over time they actually become genuine friends despite the bickering.
Content compiled by AnimeList.moe from publicly available sources.