Then you should keep reading cuz that's what she does. However... child is a bit much to describe her younger brother. He's around 12, 13yo not 9. Yeah he can grow and change but she needs to give him a strong enough reason to. And his behavior is so bad the "gentle parenting" is off the table. Even if she trued he didn't respect her enough for it to work. You can't teach someone that thinks they're above you so first she had to show him that she's the one in control and not him.
Also, you seem to forget but mc is actually 16, 17... not much older than him and not an adult yet. She might have been a recently graduate in her past life, around 22, 25... and she just remembered all that... but even so that ain't a age where most people would be wise enough to raise a pre-teen... and she's his sister not his mother... and it's not really her responsibility to fix him... in that situation and fighting for the position of heir it wouldn't be weird even if she offed him or dispatched him to god knows where...
Lastly about the father... again... she's 16-17... not an afult yet... and her father is strong AF... and competent enough that his position and control over the family is stable as hell... not someone she can get hid of or push aroud as easily as the brother. She getting him out of the house for long enough so she can take control of things is already a major win... but with her personality... you bet that if she was strong enough she'd force him into retirement without thinking twice.
So yeah... her mother got off easily cuz she deserved to be bish slapped to death with that mentality of hers... and the father deserves to at least be one of those "my adult child doesn't speak with me" parents... but the brother being young doesn't mean he doesn't deserve to be appropriately punished for his bad behavior. Tbh if it was me he'd probably lose his life in some way as soon as the father was out of sight...
╮(￣▽￣)╭
Dropping this, 8 chapters in and i find the fl so immature. Like I get that her parents treated her unfairly but be for real here, your brother is a child why don't you get your own back against your dad not your little brother. He may be childish with bad behaviour but that's because of the parents, he's still a child he can still learn, grow and change.