Just caught up from the start, here's my random theory. Nagi's father REALLY wants the Amano and Umino families connected, for some reason (regardless of whether he intentionally orchestrated the baby swap), and I don't buy that it's just due to the Nagi/Erika switched at birth thing, since for some reason he suggested that Nagi marrying Sachi works as well (sure it joins the families, but wasn't the point to marry the switched kids?). To our knowledge, the Umino family is poor though, so it's a weird choice for a hotel tycoon's son's arranged marriage.
I think there's something important about the Umino family that we don't know. All we were told is that the Umino parents are ex-delinquents (from how Nagi/Sachi were raised). Based on that, I'm guessing that maybe the father is related to a big yakuza family (making Nagi's reference to a yakuza fiancee ironic in chapter 1, haha), but that he decided to live a humble clean life and separated from them, possibly when his kid was born. Obviously neither Nagi nor Sachi would know anything about this. The reason for Amano wanting the Umino family connection could be that it'd allow him to expand his hotel chain into some territory controlled by the Umino yakuza family.
I'm less confident about this part, but if Nagi's brother figured out what the father was planning, like possibly that he planned to have him marry Erika, who was raised as his sister, that'd be a pretty good reason to run away. That'd make Nagi+Erika a backup plan, and Nagi+Sachi the backup backup plan (Sachi+Nagi's brother a 4th option?? just wait till they coincidentally meet). This part sort of assumes that the father intentionally swapped the children at birth, which makes me less confident about it. Like how exactly would you plan to switch children at birth? Keep track of the other family's pregnancy and somehow sync your wife's delivery? Or was it spontaneously executed upon seeing a baby's name in the hospital? Hard to believe it was a premeditated 16 year plan. It's much more believable that it's opportunistic upon learning about the accidental swap. I also feel like we just don't have enough info to make a good guess on Nagi's brother in general.
Anyway this series is pretty fun, wasn't expecting to be theory crafting when I picked it up.
P.S. Hiro is worst girl, she's controlling and selfish and probably hypocritical because I think she has plenty of secrets of her own that she doesn't share with Nagi.