I don't think Asa's mum was a villain. She was a bad person to her sister, she made mistakes as a mother, but she did care for her daughter, and I think she cared for her sister as well. She was just a mess, psychologically, like a lot of people are. She wanted to be the sort of person who could tell her daughter to be whoever she wanted to be, but in reality she was controlling and needed the people around her to reflect her ideals of how the world should be. But she could never fix that, because to fix it she'd have to recognise that she wasn't living up to her ideal in the first place, which she was psychologically incapable of.
I think the reason Asa's mum hated her sister was in part because she secretly admired Makio for being her own person, and for ignoring the unreasonable ideals of others. But she couldn't admit that to herself, because that would make her weak, and the life that she was constructing for herself, which aligned with what she thought the social ideal of a perfect/proper life was, meaningless. So she simultaneously admired and resented her sister for proving her outlook on life wrong.
In short, she should have seen a shrink, because she was seriously messed up in an unfortunately very common way.
Edit: After reading the next chapter, I think it backs me up a bit.
Asa's mum became trapped in the perceptions of others, to the point where she lost her control over herself because she was so caught up in the process of living up to the ideal she'd created from her perceptions of the expectations of others. And that made her desperately unhappy, and she knew that that was a bad way to exist, which is why she told Asa to be whoever she wanted to be, and that she'd support her whatever that was.
But because it was so deeply ingrained in her, she couldn't help but project those same ideals onto Asa, unthinkingly, in small comments, or in how she reacted to her daughter's decisions, or in the ways she tried to exercise control to bring Asa in line with that ideal, just like she brought herself in line with it.
She was probably aware of this dissonance on some level, maybe not consciously, but it's probably part of what motivated her to write that diary for Asa to be read when she turned 20. A sort of apology and explanation for the way she was. "I wanted the best for you, and I love you, but I probably failed and hurt you in ways I don't even realise, or can't bring myself to", that sort of thing. Also probably a way of achieving a candid intimacy with her daughter that she would have been incapable of in person, due to all of the masks and barriers within herself she must have created to maintain the ideal she had constructed for herself.