oh this... this is a very old question, i am so sorry. it's probably fairly obvious, but i primarily associate the domans with koharu because she IS doman. she grew up as friends with hien and yugiri (albeit a little older than them) and considered gosetsu to be like a grandfather. yotsuyu she has very complicated feelings about because koharu considers her to be a "what i could have become" scenario, but also yotsuyu very much represents the culmination of koharu's own mistakes because she was just as responsible as the rest of doma for what yotsuyu became. it's not something i've really 100% decided on being canon or not, but i've been thinking a lot lately about how there was a chance she knew yotsuyu and asahi as children, which would have greatly impacted her (and her interactions with both of them) in the far eastern arc in stormblood as well.

oh shit i didn't think i'd actually get any questions here so i forgot to check it but UHHHH. honestly i think it would probably be the vault.

she'd consider trying to save her family, but her parents were very stubborn people -- her father especially. if she wasn't able to convince them to leave with her the first time around, she likely wouldn't be able to do it given a second chance, either. she'd also, very briefly, consider going back to the point where she decided to leave doma and just... not leaving at all. ultimately that would result in not just her own death but the deaths of literally everyone she ever came to know and love after leaving.

but with going back and changing the events of the vault, she'd be saving the first person she considered a friend after her arrival in eorzea. the first person to treat HER as a person and not as a weapon or look down on her for being an adventurer(/mercenary). she'd only have a vague idea of what the ripple effect of saving haurchefant would entail because of the echo, and what little the echo shows her isn't enough to dissuade her. it's a sacrifice she's willing to make.