Spoilers.
Before I get into this, I just want to clarify that I am, in no way, excusing or justifying abuse. I may not have been a victim myself, but many people that I know in real life and care about have been victims of abuse or neglect.
I don't like Endeavor. He's an on fire garbage can, but I do think he's an interesting character and in my personal opinion, his character development so far was well done and I actually liked his arc. You don't have to agree with me, of course, and I don't think Horikoshi expects anyone to just like him now.
I think some people misinterpret what his initial goal was. His goal wasn't to simply usurp All Might's position as the #1 hero and be the most popular. It was to surpass him in strength, which is something no one else thought was possible and no one else attempted to do, according to Hawks, and like Hawks, I honestly find that kind of admirable. Had more people actually tried to get on All Might's level, the backlash of his inevitable retirement wouldn't have been as extreme. However, Endeavor was overcome by this ambition to the point of obsession, and he was held back by his own mindset. When he decided there was no way he could do it himself, he arranged his marriage with Rei to have strong children that would be able to achieve his goal. Stuff like this happens in real life too, where parents pressure their children to achieve what they couldn't, and can be harsh when they don't meet those expectations. You see it in beauty pageants and other competitive stuff like that.
When All Might used up the last of his power and was forced to retire and Endeavor became #1 by default, he was furious and refused to accept it, because it wasn't how he wanted to earn the title and maybe he thought he didn't deserve it then, similar to how Bakugo wouldn't accept his victory at the sports festival after Todoroki seemed to give up. It must have dawned on Endeavor that he now has a massive void to fill left by the former symbol of peace and pillar of justice, so he swallowed his pride and asked All Might for advice and what it really means to be #1, and then vowed to Shoto that he would become a hero and a father that he can be proud of. Shoto's still bitter, and he has every right to be, so he just brushed it off, but it's a big step for Endeavor.
Going from the experiences of abuse victims in my life, everyone reacts to it differently. Rei and Fuyumi seem okay with letting Endeavor back into their lives despite their past abuse or neglect, maybe because they just want to be a happy family or recognise and appreciate that he's trying to better himself. Natsuo, who I can relate to the most, wants nothing to do with him and is being protective of the rest of his family. Shoto still seems resentful but relatively indifferent, but he obviously still acknowledges his change of heart and cares seeing as he cheered for him during his fight with High End and doubled over in relief when he survived. Fuyumi seems to be taking on the role of a peacekeeper, but she shouldn't expect her brothers to forgive their father so easily, and I don't think Endeavor expects them to forgive him anytime soon either. All these different reactions are understandable and pretty true to life from what I know.
Also, Dabi, who I heavily assume is Toya at this point, probably ran away from home, died his hair as a way of disowning Endeavor, and resonated with Stain's ideologies because his father was exactly the type of hero that Stain despises.
Endeavor's family can choose whether to forgive him or not. Nothing can erase or justify his actions in the past and they shouldn't be forgotten, and it may take a long time for Natsuo and Shoto to forgive him, but he can still give them a better life for the future. He got a new costume, maybe symbolising his desire to change for the better, and his scar which is on the same side as Shoto's shows that he is paying for his past actions. I also think someone once said that people who need redemption the most deserve it the least.
Sorry this got rambly or seemed insensitive in the slightest, but feel free to let me know your own thoughts in the comments.