Oskar's Mom is a busy attorney who's somewhat awkwardly trying to fill the role left by his father, tucking him in at night, offering to read to him and check the New York Times for mistakes. She and Oskar have had a tense relationship ever since Dad's death. Oskar thinks that, if someone had to die, Mom would have chosen Dad to live over him.
If she could have chosen, it would have been my funeral we were driving to. (1.16)
But maybe that's just because Oskar would have chosen Dad over her. He actually says this to her point-blank:
"If I could have chosen, I would have chosen you!" (7.144)
Ouch. That really hurts her. "You can't take something like that back" (7.152), she says sadly in a scene that makes us never want to have children.
Another thing adding to the tension between mother and son is Mom's relationship with Ron, someone she met in a grief group (but Oskar doesn't know that). We're not sure if she and Ron are sleeping together or not, but Oskar thinks they are. He wants to tell Ron, "You're not my dad, and you never will be" (1.6). Oskar can't understand why (or even if) she's "moving on" so soon. He doesn't accept that she might need some comfort, too. He thinks she just doesn't miss Dad as much as he does.
Oskar hasn't forgiven his mother for not being home when he got home from school on the worst day. He thinks that maybe things might have turned out differently for Dad if she'd been home. At the very least, she would have heard the messages and picked up the phone.
For much of the novel, Mom's on the fringes of our story. She seems like an absentee parent. She doesn't even ask Oskar where he's going when he leaves the apartment and ventures out into New York City by himself. (He's only nine; what could she be thinking?) Even Oskar notices her laissez-faire attitude toward parenting:
Why didn't she ask me more? Why didn't she try to stop me, or at least keep me safe? (15.19)
By the end of the book, we find out that Mom has known where Oskar's been going the whole time. She knew about his quest to find all the Blacks, and she called them ahead of time to let them know he was coming and ask them to treat him well. In fact, we can read between the lines throughout the novel and see that his mother has been paying very close attention to him all the while. She sees the bruises; she gets him into therapy; she talks with his Grandma about him; she monitors his journey.
Oskar's emotional immaturity is clear from the way he totally misunderstands his mother. He rarely sees her crying, and concludes that she's forgotten his Dad and is just moving on with her life and having fun with Ron.
"You think because I laugh every now and then I don't miss Dad?"
She said," I cry a lot, too, you know." "I don't see you cry a lot." "Maybe that's because I don't want you to see me cry a lot." "Why not?" "Because it isn't fair to either of us." (7.124-125)
Mom also has some mild PTSD symptoms. When Oskar wakes her up:
I touched her incredibly gently. She jumped up and said "What is it?" I said, "It's OK." She grabbed my shoulders and said, "What is it?" The way she was holding me hurt my shoulders, but I didn't show anything. (5.65)
Mom's a more private person in general than Oskar's father, who showed his affection and interest in a very engaged, hands-on way. She's also more spiritual than Dad, who was a confirmed atheist and rationalist. Here's one of those typical mother-son discussions about mausoleums and caskets:
"It's just an empty box." "It's more than an empty box."
Mom said, "His spirit is there," and that made me really angry. I told her, "Dad didn't have a spirit! He had cells!" "His memory is there." "His memory is here," I said, pointing to my head. (7.116-117)
As Oskar tells us later, he used to be an atheist like his Dad. Apparently, he's moved away from that somewhat, and it could be his mother's influence.
After Oskar digs up Dad's grave, he returns home to his Mom, and there's a very intense emotional moment for both of them. They cry together—a lot—and Mom shares her own secret, that she spoke with Oskar's father when he called her from the World Trade Center on 9/11. She tells Oskar that Dad told her he had gotten out and was walking home. He didn't want her to worry, but he knew she knew it wasn't true.
Since we see Mom mostly through Oskar's eyes, it's a skewed picture. Once she speaks for herself, she becomes a much more sympathetic and three-dimensional character.