The story Doug reads to the homeless woman, is a real book by Adam Mansbach called "Go the Fuck to Sleep," and although the book is (more or less) written in the style of a children's bedtime story, it is - in reality - written for the parents of children who won't go (the F***) to sleep.
The homeless woman Doug recruits for his shelter, played by Tammy Caplan, was in the halfway house in New York with Nancy in A Hole in Her Niqab (2011).