Abigail is Susie's mom and a complicated woman. Her love for Susie is apparent in her intimate knowledge of things Susie related, as detailed to Len Fenerman. But, as Susie had already learned from photographing her mother, the role of perfect wife and mother was something of a disguise, masking other desires that rebelled against domesticity.
When Abigail learns Susie is dead, she can no longer keep up the façade. She becomes an adulteress (to get all Scarlet Letter on you) and then an abandoner of her family. Susie can relate to her mom in both instances. She recognizes her mother as an independent person, with the freedom to make her own lifestyle choices. She understands that her mother has her own way of dealing with grief, loss, and figuring out what she wants. Jack, Susie's dad, is likewise understanding of Abigail (though he doesn't know of the affair).
But Lindsey and Buckley, not so much. Of course, it's easier to have your mom leave home if you're dead than if you're alive, grieving, and very much in need. Chances are Abigail wouldn't have been the mother they imagined in their fantasies.
She returns eight years later after eight years, after Jack has a heart attack, and she is able to see how much she's loved Jack all along. She's learned about herself while she's been away, and she's learned about him as well. Ironically, only when he's laid low from the heart attack does she realize how strong he is and how strong he's had to be with her gone.