From what I recall, she was pregnant from <PERSON>, but for some reason that I don't recall, she left him for another man with whom she didn't cheat on <PERSON>. <PERSON> asked for a paternity test.
It seems to me that these call are her way to give <PERSON> a chance to make amends.
EDIT : Here are a few quotes from the book to expand on what I already wrote :
They started drifting apart due to <PERSON>'s job.
She told him he was becoming hard, intractable, reductive in his thinking. And he didn’t respond because there was nothing to argue. The question wasn’t whether he’d become those things, but whether the becoming was a positive or a negative.
<PERSON> had an affair, and fell pregnant, but it's not clear from whom. And that's what makes it even harder for <PERSON> to accept.
Still, he probably should have seen the affair coming. Maybe he did. And maybe it wasn’t the affair that truly bothered him, but the pregnancy that followed.
<PERSON> discovering the affair she’d had with an actor, of all things, starting to ask her, “Whose kid is it, <PERSON>?” and <PERSON> coming back with, “Take a paternity test, you’re so worried.”
<PERSON> didn't take the news too well, and I assume they broke up at this point.
And had <PERSON> hurt her? Well, yeah, of course. When he first found out about the affair, he’d come damn close to hitting her, pulling back his fist at the last moment and putting it in his pocket, <PERSON> seeing the urge in his face, though. And all those things he’d called her. 86
Jesus.
<PERSON>'s phone call are her way to let <PERSON> fix what he has broken, which he does in their final phone call.
He said, “I’m sorry.” And <PERSON> spoke. “For what?” “For putting it all on you.” “Okay…” “Hey—” “Hey—” “You go ahead,” he said. “I…” “What?” “I…hell, <PERSON>, I’m sorry, too. I didn’t mean to—” “It’s okay,” he said. “Really.” He took a deep breath, sucking in the soiled, stale-sweat stench of his cruiser. “I want to see you. I want to see my daughter.” And <PERSON> answered, “How do you know she’s yours?” “She’s mine.” “But the blood test—” “She’s mine,” he said. “I don’t need a blood test. Will you come home, <PERSON>? Will you?” 417