For a three-act plot analysis, put on your screenwriter’s hat. Moviemakers know the formula well: at the end of Act One, the main character is drawn in completely to a conflict. During Act Two, she is farthest away from her goals. At the end of Act Three, the story is resolved.
Act I
While Father is away on a voyage to the (brrr) Arctic, Mother discovers a newborn baby buried in the backyard. It's like the world's creepiest Easter egg hunt. The father of the baby, Coalhouse Walker, visits the family weekly to see his fiancée and the baby. When his car is vandalized on a trip home and his fiancée is killed, he vows revenge on the vandals.
And that's just our main story. Tons of stuff is happening elsewhere: Tateh rises from living in grimy tenements to making flipbooks, Evelyn Nesbit is all sorts of tied up with her husband's trial, and Freud visits America and does not like it one bit.
Act II
Coalhouse seeks his revenge on the city, bombing firehouses and killing firemen and policemen. It's like the world's goriest Valentine to his murdered sweetheart. With his gang, he seizes the J.P. Morgan Library and holds its contents.
Father and Mother's marriage is puttering along in a yawn-inducing manner (um, maybe because their only names are "Mother" and "Father"?), Tateh's career is on the rise, and Mother's younger brother (yeah, his name is Younger Brother) joins forces with Coalhouse. There's probably someone in America that's just having a calm, lovely time, but we surely don't see it. Everyone we meet is frantic and getting their drama on.
Act III
Coalhouse gets his car back but is shot and killed by the police: they claim he was running from them but he absolutely was not. He's only the first character we see kick the bucket in this morbid Act III: as the Ragtime era draws to a close and World War I begins, Father dies aboard the Lusitania and Younger Brother dies in Mexico.
Mother later marries Tateh, a Jewish immigrant, and they move with the children to California. Sheesh. At least someone got their happy ending.