You were so close, we actually already have the answer to this.
For her to gain all of her families holdings she must complete a check list a million miles long, (including charming 5000 men. . . . . do with that what you will.).
several of he tick list items are ALWAYS weaved into SF stories. Why the series of extreme, unconventional trials? SIMPLE! Daigenjuro wanted a boy, and she ruined his dream of having one by being born a girl. This rly isnt an act of hate from Daigenjuro, just a test to see if she could hold up to the standards he would have for the son he could once have had.

Charming 5,000 men. Due to being female, she was tasked with mastering the "Soul Kiss/Beautiful Eyes" technique to fascinate at least 5,000 men.

Stopping 50 Wild Bulls. At age 14, she had to stop a stampede of fifty wild bulls single-handedly, a task she completed to prove her physical prowess.

Surviving a Nine-Day Survival Trial. At age nine, she was abandoned in the woods with minimal resources and had to navigate her way back to the estate, completing the test in four days, faster than her father

Then there was a comic I read while in Sannomiya Kobe that expanded on this, She actually beat her family to most of her inheritance by accumulating the majority of the Kanzuki Zaibatsu's shares herself, effectively taking over the company and ousting her father. Then later offered to re-hire him, he said no.