Corinne is Bart's mom, and since she's super close with her son (a.k.a. our narrator), she's the character we understand best besides Bart himself. But that doesn't mean we know a whole lot about her. Instead, like Bart, we primarily understand her through her problems.
Corinne is a private person—so private, in fact, that she keeps the fact that Bart's dad's left her a totally secret from her family (with whom she's very close) for the entire six months leading up to the attacks on September 11. That's dedication to privacy, yo.
And after her estranged husband's tragic death, she only becomes more private, withdrawing even from her son. It's not that she's selfish, per say, she's just super depressed. But unfortunately, her depression feeds into Bart's sense of isolation. As Bart expresses:
Mom was not in her most reliable get-out-of-bed-bright-and-early-morning mode […] In fact, we'd both slipped into a kind of dream state. We didn't go out much, we mostly stayed home with the curtains closed and lay on my mom's king-sized bed. (3.7)
Misery may love company, but this sounds like pretty miserable company for Bart to be stuck keeping, especially since it's pretty much the only company he has. So it goes with depression, though.
The first thing that helps lift Corinne's depression is the news that Bart has received a full scholarship to an elite private school. (Yep, that would be Baileywell.) She sees it as "something good coming out of something bad" (3.21), and the news is "the first thing that had gotten [her] excited, or even interested, in weeks" (3.15). As a result, Bart feels like he can't fully share his dread about being pulled from the public school he knows and dropped down in a place that's notorious for bullying. And further, once the bullying starts, Bart keeps it from her because he's afraid she'll worry.
Once Corinne returns to work, she seems to cheer up considerably. Though she and Bart have a good relationship, she's oblivious to the bullying Bart's dealing with at school until he gets caught vandalizing a car and confesses the whole situation. She's furious—not with Bart, but with Dr. Bratton, the headmaster, for letting this happen.
With that, while Corinne's problems might not all be solved, she comes roaring to life, like a mama bear erupting from hibernation. At the school meeting, she is blazing with righteous indignation on Bart's behalf. And then later she comes through for Bart when his friend Nola dies. Finally, at the very end, she's able to open up to Bart about her sadness about her husband's death. "You think you'll feel this way forever," she tells him. "But you won't, honey. Little by little, day by day, you'll feel better" (13.48). Sounds like Corinne knows what she's talking about.