It seems pretty clear that Maya's father threatened to disown her if she didn't behave 'properly.' She flat out tells us he gave her an ultimatum when we first meet her, Maya and Josy repeatedly state he can't know the two are living together, and we know he asked Derek to keep an eye on her.
You can see further evidence in Maya's graduation picture, where her dad is hugging Derek and smiling while Maya is on her own looking sad. Or even in Maya's "Not the daughter I wanted" rant at the MC in Episode 2. It seems pretty clear that Maya isn't the one who abandoned her father.
As for Maya being envious, maybe. She says she's happy for Josy, but she is clearly upset that she feels any negative emotions about it. We could call that envy, or we call it something more like melancholy. It really depends on just how much Maya resents Josy for getting a loving father, rather than how much Maya just wishes she didn't have to fight her own father.
I guess I don't see Maya's actions as all that bad. As was pointed out, by the time Maya walks off it's clear Josy will not need emotional support. So it's possible Maya left so as not to ruin Josy's mood, rather than because she couldn't stand watching Josy get to be happy. IMHO, I'm inclined to give Maya the benefit of the doubt because I think her fundamental point is valid: parents ARE supposed to be there for their children, and Maya's dad isn't.
I think it's easy to overstate just how weak Maya is relative to the MC. It was only last episode that the MC spent two days sulking around because his girlfriends were cheating on each other with him. Even with her tears, Maya seemed to handle that better than he did.
Frankly, all the LIs tend to rely on the MC for emotional support, and I doubt that trend will stop any time soon. Maya's been doing it a lot lately, but her problems are also more blatant than the others (at least until we learn Bella's backstory).
EDIT: In other words, more or less what
Holy Bacchus said.