Deanna's mom is perhaps the most tragic character in Story of a Girl, and unfortunately for her, we never get to see any real change in her life. She works a low-paying retail job at the now-defunct department store Mervyns, and Deanna wonders,
What if Mom didn't have to work at a department store, with people complaining all day about stuff they'd bought, or leaving piles of clothes on dressing room floors for her to pick up? Would she look so gray and tired? (5.26)
No, she probably wouldn't, but she's not making any effort to do anything about it. You can see that Deanna's mom, like Deanna, has totally given up on a better life—it shows in both her physical appearance and her willingness to stay at a job she hates. Of course, we can't forget that studies have shown that poverty actually decreases a person's mental capacity to handle problems—so it might not be Deanna's fault that she's lost the will to live.
Deanna's mom is just trying to keep her family together, or at least keep it from falling any further apart. She's always either ignoring or making excuses for Deanna's dad's behavior, and she tries to smooth over fights by offering food, from casseroles to instant oatmeal. As much as Deanna wants to bust out of that family and that house, she feels bad for her mom:
I could see it all like a movie on a screen: her, alone with Dad for the rest of their lives, the house staying exactly the same (down to the last detail), shabby and worn-out, all the stains and holes and leaks showing, green shag carpet forever. (3.54)
It's just one more example of how the whole Lambert family has pretty much given up and accepted their lot in life.
As much as we want to think there's hope that things could be different, Mom's not making any moves to make them that way. She's just going to work, coming home, feeding and cleaning up after everyone to keep them from fighting, and getting up the next day and doing it all again. As awful as it is to think that her life will continue like this forever, unless she stands up for herself and makes some drastic changes (for example, leaving her husband and going to school), Deanna's probably correct in her belief that it will.
When Deanna looks at her mom, she likely sees a woman who has let Ray beat her down, just like he's beating Deanna down. After all, we never see him show any of his family members any affection, with the exception of the one brief moment when he holds April before handing her back to Darren. How can Deanna possibly feel hopeful when she's surrounded by hopelessness?