Why do you think Vanetta’s public defender failed to mention that she was attending GED classes, providing childcare, and looking for housing every morning? How might that information have impacted her sentencing?

Like most poor people who end up in court, Vanetta has to rely on a public defender to make her case. Public defenders' offices in most states are notoriously understaffed and under-resourced, which severely impacts their ability to provide good quality legal counsel to their clients. And this is a possible factor in relation to Vanetta's case.
She's up before the court on a very serious charge: armed robbery. Despite making an impassioned plea on his client's behalf, the public defender neglects to mention that Vanetta's been getting up at 5 every morning to look for a place to live, attending GED classes, and caring for children. These are all potentially mitigating factors which one would've thought Vanetta's attorney might have raised. But he doesn't.
Possibly this is because he figured that such an approach wouldn't work with the judge. And it turns out that he's right. Because although the judge accepts that poverty was a factor in Vanetta's committing the crime, he doesn't treat it as a mitigating factor when it comes to sentencing. His reasoning is that Vanetta will still be poor if he lets her go, and what's to say she won't then commit another serious crime? So the judge sentences Vanetta to eighty-one months in jail.