A stray cat narrates the story of the Willoughbys, once an adventurous and loving family for generations. The present-day Mr. and Mrs. Willoughby are too enamored with each other to care for their four children: eldest son Tim, who tries to keep his siblings out of trouble; middle daughter Jane, whose beautiful singing is silenced by her parents; and the inventive but “creepy” twin boys, both named Barnaby. The parents mistreat and neglect the children, refusing to give them food and punishing them by making them sleep in the coal bin. After Jane and the twins find a baby abandoned outside, their parents kicked them out of the house until they return without the child. They leave the baby, whom Tim names “Ruth”, on the doorstep of a candy factory and the owner, Commander Melanoff, takes her in.
To rid themselves of their neglectful parents, the siblings send them on a “dangerous vacation” by fabricating a travel brochure of volcanoes, bears, and other hazards. As the children celebrate their freedom, a nanny hired by their parents arrives and wins over everyone but Tim. Learning about Ruth, Nanny takes the children to Melanoff’s factory. After saving Ruth from the assembly line, Nanny realizes the child is safe with the loving Melanoff. Mr. and Mrs. Willoughby, having survived the various danger, not wanting to go back to their children but short on funds to continue their trip, sell their house online. They also inform Nanny in a voicemail, which Tim overhears. Believing Nanny is in league with his parents, Tim reports her as a “bad nanny” to the sinister Orphan Services.
When their parents’ realtor arranges an open house, the siblings scare off potential buyers with a series of traps. Nanny frightens away one last family, convincing Tim that she means well, but Orphan Services arrives. The head agent recognizes Nanny as Linda, an orphan who never found a family who wanted her. Learning that Tim called Orphan Services, Linda leaves and Jane angrily chastises Tim before the siblings are separated and taken to foster homes. Tim keeps running away from his foster families, discovering in the process that the Willoughby mansion has been sold and demolished, and is eventually confined at the Orphan Services center. The cat finds Linda and brings her Tim’s signature helmet, convincing her to reunite the children.
Linda breaks Tim out of Orphan Services and collects the siblings, and Tim apologizes to Jane. He suggests that they find their parents in order for Orphan Services to leave them alone. Linda and the siblings enlist Melanoff’s help to construct a candy-fueled dirigible to travel to “Sveetzerlünd” (a parody of Switzerland), where their parents are scaling the “unclimbable Alps”. Taking flight without Linda, Melanoff, and Ruth, the siblings reach Sveetzerlünd. They follow a trail of their mother’s yarn to the top of the mountain, where they find their parents nearly frozen to death. The siblings save them, confessing that they sent them away but hoping to reunite as a family. Unchanged, Mr. and Mrs. Willoughby abandon their children and take the dirigible, but cause it to fly out of control and crash. The siblings prepare to succumb to the cold as Jane sings, but they are rescued by Ruth, Linda, and Melanoff.
Linda and Melanoff adopt Ruth and the Willoughby children, all living at the candy factory as a loving family. Meanwhile, Mr. and Mrs. Willoughby survived the dirigible crash, floating at sea, and are presumably devoured by a shark. In a post-credits scene, the cat cleans himself until noticing the audience.