We'll probably get to that in the manga very soon, but if you can't wait...What’s going on with the mom? Classic case of caring more about “business” than parenting?
Her mom got very stressed from being a single mother raising two kids. One time when FMC was 2 years old and had a tantrum, her mom snapped and hit her with the flat of her hand, and it resulted in FMC hitting her head pretty hard and bleeding a lot. Her mom panicked and called an ambulance. It ended up being a minor injury that didn't leave a scar or anything, and FMC doesn't even remember it because of how young she was, but her mom still remembers, and it makes her feel guilty about it every time she sees FMC. So rather than try to make amends like a rational human being would, she takes an "out of sight, out of mind" approach by trying to push FMC away, which is why she's so cruel to her.
And as for how the story leaves it unresolved...
FMC's sister tells her about this as they're on their way home (probably in the next chapter of the manga), and when she gets home she confronts her mom with MMC at her side for moral support. She tries to make peace, but her mom rejects her and tells her to leave. FMC says that she doesn't want to leave, and her mom basically says "fine, if you won't leave, I'm leaving" and storms out. And that's pretty much where volume 2 of the LN leaves things. Her mother doesn't return home but is still working as her sister's manager.