This is an excellent question! Sebold deals with these two characters in totally different ways, in my opinion a genius stroke of word choice, directly reflecting the characters thoughts themselves. Let's deal with them separately: Abigail and then Jack.
Abigail deals with Susie's death by completely withdrawing from family life (first through washing the dishes, later by having an affair, and finally through flight). It is through Abigail's characterization that I first noticed the genius of Sebold's writing. Abigail reveals nothing through words or thoughts, only through actions. As a result, as a reader, I was continually struggling to understand her position and her thought process. Ah, that's as it should be: Abigail withdraws from family, reader withdraws from Abigail as a result of diction. In fact, although her actions reveal Abigail questioning her parenting (with her flight from the family to the other side of the country being the ultimate result), there is very little about her thoughts in regards to this! The only inkling can be found when Abigail returns home only because of Jack's heart attack:
She now knew that being a mother was a calling, something plenty of young girls dreamed of being. But my mother never had that dream, and she had been punished in the most horrible way for never having wanted me. (266)
Jack deals with Susie's death by throwing himself into the investigation of his daughter's murder all the while keeping Susie alive with his devotion. Jack shares his thoughts continually, so there is a lot more evidence in the text of him questioning his parenting. First, Jack struggles with how to tell Buckley about his sister's death:
"What's wrong with Mommy?" Buckley asked. Together tehy watched my mother, who was staring into the dry basin of the sink.
"How would you like to go to the zoo this week?" my father asked. He hated himself for it. Hated the bribe and the tease--the deceit. But how could he tell his son that, somewhere, his big sister might lie in pieces? (63)
The ultimate in Jack questioning his parenting revolves around what I believe to be a very normal feeling of guilt:
The guilt on him, the hand of God pressing down on him, saying, You were not there when your daughter needed you. (58)
Poor Jack. My heart went out to him during this entire novel. Desperately trying to find his daughter's murderer. Keeping Susie's memory alive with is very breath, even through clinging to her old clothes. *sigh* I'm afraid I looked at Abigail in disgust through most of the novel. How dare she leave her husband and children to escape the situation. Yes, yes, she is grieving in a different way. I don't care. As a Mom, you don't have that option. Lindsey is okay, but Buckley is permanently damaged as a result. Disgusting. Of course, this is from a fairly new mom's point of view. An interesting idea for a discussion question, actually!