@luminary
Someone who is a genius does not make them genius at everything else, like people skills.
Besides, chapter 1 kind of tells you what's going on. From day one, the children refused to listen to her. The youngest children still mourned for their real mother and refused to accept her as their new mother. She still believed she can work it out. 2nd child seems to have bullied her. She starts to lose hope in having all the children accept her. 1st child, the eldest, accused of her of many things and said that if it wasn't for her, their father would have requested to see his children on his death bed instead of her. She lost all hope to become close to the children. Even then, she continues to full fill her duty to protect them even when she was a child herself when she started, basically being sold off by her own family AND mocked for her aspirations.
In that same chapter 1, after some time had passed, the children finally realized their mistakes with their assumptions about her. "We were wrong! Let's go apologize now!" But it was too late as she had already died. It's truly tragic. If she had continue to try, maybe the outcome would have been different. If the children have tried to understand her, maybe the outcome would have been different. But tragically, they're all children. And even more tragically is that one of the children, her, have to take upon such a burden at such a young age.
EDIT: OH! Apparently there is a novel, which is the source. The manga's prologue and chapter 1 is basically the novel's prologue. Here's basically the written summary of the prologue in the novel. And it's basically what I wrote but with a lot more details as to what happened. Regarding her relationships with other men that her son hated her for, apparently she did to use those people to protect the household. Damn, that really, really sucks for her. I guess reading chapter 3 kind of makes sense. Her children hates her but it seems like other the butlers and maids seems to actually understand her and were worried. They knew she's not a terrible person and it was all done to protect the household.
https://forum.novelupdates.com/posts/5113456/
EDIT2: Don't read the rest of the comments unless you're ok with spoilers for future chapters.