Mikoto was Sasuke's mom btw. Watching the latest filler episode, there was a scene that struck me: Mikoto seeing baby Naruto in the hospital and sighing. Would Sasuke's family have adopted Naruto? Obviously they couldn't, because handing the Kyubi jinchuriki to the Uchiha is not something Danzo would let fly. But if Minato had sealed all of Kurama within himself before dying and Naruto was never made a jinchuuriki, would Fugaku and Mikoto have adopted Naruto? How weird would it be for Sasuke and Naruto to literally be half brothers? Would Itachi have killed Naruto during the massacre?
No, they obviously didn't and therefore decided not to. Mikoto knew that he was Kushina's son, but Fugaku probably wouldn't have allowed it anyway. He originally pushed his older son and ignored his younger son. Then, Fugaku gave up on his elder son once he pretty much informed him that he didn't support the clan's way of thinking and then turned to the younger son as a replacement. Clan>kids to Fugaku. Adopting Naruto wouldn't benefit them as harsh as that sounds, Fugaku wouldn't want a non-Uchiha.
Itachi stated that he didn't kill Sasuke because he was too young and innocent. He didn't know anything about the coup, so there was no reason for him to die. Naruto is the same age as Sasuke and wouldn't know either. Naruto would be fine.
And Mikoto and Kushina seemed to be on pretty good terms with each other. They would have chitchats and looked to be familiar with each other, maybe they were best friends.