The Todoroki Family currently consists of Enji Todoroki, his wife Rei, and their four children.
The Todoroki family is not a typical loving family, but a forced, abusive, unloving one from the start.
The biggest conflict of the family comes from Enji's treatment of Shoto. Ever since a young age, Enji has put his youngest child through a inhuman training routine with the intent of raising someone that could eventually surpass All Might. As a result, Shoto grew resentful of his fate as Endeavor's eventual successor and started rejecting all aspects of himself that tied him to his father, namely the fire half of his Quirk. It took a confrontation between Shoto himself and Izuku Midoriya for the former to accept his power as it was.
Aside from Shoto, it would appear that Enji treats his other children neutrally. He doesn't give them the harsh training that Shoto goes through nor does he seem to treat them properly as a traditional father would to his children, calling Shoto's brothers as 'things'.
Natsuo hates Enji and has not forgiven him for the treatment he gave them all those years. Fuyumi has the best relationship with her father out of all the children and wishes for a normal, well-adjusted family. Shoto himself now has a mixed opinion on Enji, thinking highly of his hero work, but poorly as a parental figure. While he does not expect to be ever forgiven by his children and wife, Enji does wish to make up for all the wrongdoing he has ever caused to them.
Enji Todoroki used his power and influence to force a marriage with his future wife Rei. The purpose of this marriage was an attempt by Enji to conceive and raise a child with a powerful Quirk in order to surpass All Might. The marriage between the two was an unloving one and only done for Enji's personal desires.
The two had conceived one daughter and two sons before the hybrid Quirked Shoto was born. Beforehand, Enji trained his oldest child, Toya, to be his successor due to having perceived strong potential in his Quirk, which was a stronger version of Enji's own. However, because Toya did not have access to Rei's Quirk, his body could not handle the overheating caused by his flames. Moreover, Toya became disillusioned with Enji's fierce training, losing his sanity in the process and starting a forest fire so he could fake his own death within the wildfire. Toya was believed dead during that incident, with no traces of his body being found except for a small piece of his jawbone.
At the age of five, Enji trained Shoto to become a Hero through harsh and detestable means. Shoto had little interaction with his older siblings during his childhood due to his father's intervention. Rei tried to prevent Enji from making Shoto go through his intense training, but Enji refused to listen and demanded she stayed out of it.
Rei was also a victim to Enji's abuse, to the point she started becoming mentally unstable. She snapped one day when she saw Shoto's left side which reminded her of Enji and threw boiling water over him. After this incident, Enji had her admitted to a mental hospital.
Over the course of the years, Shoto continued training while also hating his father before applying into U.A. High School. Shoto later forgave his mother for her burning him as a child and now regularly visits her, showing they have reconciled.
It appears after All Might's retirement, Enji has slowly moved past his previous behavior as he thanked All Might for bringing his son to him. He later promised Shoto that he would become a better man, and tries to extend this effort to the rest of his family as well.
Natsuo and Fuyumi have visited their mother and are shown to be on good terms with her. Natsuo mentions to hardly remembering his father, showing Enji didn't put effort in raising his elder children. Rei reveals to her two children that Enji secretly visits her but they haven't met face to face.
Natsuo blames Enji for causing Toya's supposed death and is adamant on forgiving him despite Fuyumi's efforts to reconcile the family.