THAT DOESNT REALLY GIVE US ANY INFORMATION ABOUT THE OVERALL FAMILY DYNAMIC.
The clues we have make it rather obvious no? I mean there doesn't seem to be anything strange or exceptional about it. Her mother is a super typical garden-variety Asian mom who demands the best for&from her daughter and will get into fights with anyone who goes against her wishes. We see her fighting with her husband for not being a good enough father; she's likely to fight with the school teachers as well; and if the girl was into sports she would certainly fight with the coaches asking for better treatment, more opportunities, etc.! Mom characters like her are a big classic trope in tv series, comics, movies...
The child with such a mom has of course ambivalent feelings towards her.
I didnt get ANY of the rest of that information out of it. You could assume that shes strict because she doesnt let Lin Luxi go out with any friends but then you could also assume that shes protective of her safety or perhaps shes clingy. I also didnt know that it was a trope that mothers who fight with their husbands also fight with people outside of the family?? The mothers I've known in broken marriages are basically the complete opposite with other people because they put on a very strong "happy family, happy wife" facade to cover up their deeply shameful brokenness.
I guess what you're saying is that shes a "tiger parent" which is a common Chinese stereotype. I don't want to assume that just because this manhua is Chinese, I'd rather actually receive more information about it through the story. I get that we're not going to be given that information through an exposition dump which I totally respect but that one little bite of information really baited me in just to totally leave us hanging.