Events in this story are taken mainly from the 1972 movie The Poseidon Adventure. There are also two plot elements from the original novel by Paul Gallico (novel spoilers ahead):
One: In addition to the two children, Robin and Susan Shelby (Robin is the one who said "Shove it! Shove it! Shove it!" to his older sister before slamming their cabin's bathroom door in her face), their parents are also along on the cruise, and their marriage is failing; after the ship has capsized and Robin has gone missing (see below), Mrs. Shelby says some extremely cruel things to her husband in front of the other survivors, driving a final wedge into their marriage and leaving them to grieve for the loss of their son separately.
Two: They encounter another much larger group of people also trying to escape but heading in the opposite direction, when the ship's emergency lights suddenly go out, plunging them into complete darkness. This results in panic and a stampede where several people are trampled to death. By the time someone has found a light, Robin Shelby has vanished and is never seen again.
At the end of the novel, the survivors are standing on the deck of a rescue ship watching the S.S. Poseidon's stern rise high into the air (much like the Titanic did, except the Poseidon had capsized and been floating upside down for hours), before sinking beneath the waves. Robin's mother is praying that she isn't witnessing her son's death now, but just his burial.
There is an excellent fan-made trailer for the movie here.
This is the third in a story arc. In this 'verse, Kenny has been freed from the curse of endless deaths and rebirths, and has no memory of these having ever happened.
"Midnight" in the chapter titles refers to midnight New Year's Eve, approximately five minutes before the ship is struck by the tidal wave and capsized.
I don't own South Park, The Poseidon Adventure, or any of these characters, with the exception of Pete McCafferty.
Chapter 1: Midnight minus 1 day 17 hours
Chapter 2: Midnight Minus 27 Days
Chapter 3: Midnight Minus 1 Day 11 Hours
Chapter 4: Midnight Minus 11 Hours
Chapter 5: Midnight
Chapter 6: Midnight Plus 12 Minutes
Chapter 7: Midnight Plus 1 Hour
Chapter 8: Midnight Plus 2 Hours
Chapter 9: Midnight Plus 4 Hours
Chapter 10: Midnight Plus 6 Hours
Chapter 11: Midnight Plus 7 Hours