I agree she has being Kaido's child going for her, and if genetics play any role (unlikely despite a throwaway comment that goes against rest of stuff we know about CoC), it'll be even more likely.
But that's literally all she has going for her.
Strong willpower isn't related to CoC. Nor is strong will and whatnot. There are so many characters who have strong will but no CoC.
It's Conqueror's haki. A haki that Kings have; a haki possessed by people that not only have an innate ability to lead, but also a very strong desire to stand above others in one way or another and there are no exceptions.
Katakuri and Rayleigh both are second in command, and KK clearly have a desire to be stronger; to stand above others and protect his loved ones, and we don't know Rayleigh's story enough to say he's a contradiction, though he IS a great leader.
As things stand, in terms of personality and who she is, Yamato is mimicking someone else- and although I like Yamato- as far as strong personalities of a conqueror go, that's fairly pathetic. She's not even get own individual a lot of the times
She is already a follower in more ways than one. She's not like Zoro with great individual desires to stand above others and leadership... She's a follower who is following someone so much that her own dreams are just extension of that person, her own identity is his, and there is more Oden in her than herself.
She can be very strong, but unless she gets her act together and shows a hint of what a CoC user is other than "is stronk. Daughter of stronk", she's in negatives as far as this haki is concerned. No where near qualified.
I mean her ambition is literally do things Oden wanted and protect Momosuke lol. That's very close to that of any Scabbard