I have an insane theory about Yotsuha's father that I don't think anyone has brought up yet. I don't know how exactly it ties into Uichi but I do think it ties into why her father is a "horrible person", why she was in an orphanage, and why she has a seemingly deathly genetic illness
What if Yotsuha is a result of inbreeding? I can imagine it right now. Her mother was driven insane from having to carry essentially a rape baby after her own father or brother or the like did that to her. And what if Yotsuha's father is also the father of the actual mastermind?
This would explain everything: the illness from birth, her mother's behaviour, how her brother knows her father was awful, and her relationship to the mastermind, who is also using a clover symbol. The mastermind is Yotsuha's half brother - but not the one we've been introduced to. A secret other sibling who cares about her insofar as she family technically.
Now, the incest part might be stretching it a bit much, but I think I have a solid theory here with the rest of it.
Besides that, think of it - what is Yotsuha's motif? A four leaf clover - something which only exists as a genetic mutation from three leaf ones.
TL;DR the mastermind is Yotsuha's half brother, but not the one we know. There is another, and he knows Yotsuha is his half sister, but she doesn't know about him, hence why he doesn't want to hurt her. Their shared father raped Yotsuha's mom and fathered Yotsu with her, hence why her mom put her up in an orphanage and only went back to claim her later after losing it completely. To explain her birth disease, the father might actually also be genetically related to her mom, making her a product of incest, though this part is less likely, but can be given credence by the known brother saying her father was a bad person.