Chance's nickname comes from her last name, LaChance. This is a reference to Gordie LeChance from Stand By Me (1986), or Stephen King's "The Body."
The CPS worker's name is Stephen Bannerman. The surname is also recognizable to King fans as the original Sheriff of Castle Rock, George Bannerman, who appeared in The Dead Zone and Cujo and is mentioned in numerous other King books, particularly ones that take place in Castle Rock.
"The Mother" is the second episode of the season that does not feature Tim Robbins.