The start of Easter vacation finds Tracy Osborne and her younger brother, Jay, waiting for their mother, Carolyn, to pick them up from boarding school. However, Carolyn is stuck in Hong Kong, China, on business, and sends her assistant to ship the kids and their pet skunk, Duster, to their grandfather in Los Angeles, California. On the plane, Tracy and Jay decide Carolyn really wants to see them, and they dream of acquiring $1200 so they can fly to Hong Kong and surprise her. Meanwhile, J. W. Osborne, the children’s grandfather, and his butler, Jameson, complain about the children’s behavior as they pack away their breakables in anticipation of their arrival. That night, Peter, the chauffeur, drives Osborne and Jameson to the airport and they are almost hit by a Volkswagen Beetle occupied by Duke and Bert, thieves dressed as maintenance men. After rear-ending a pickup truck, Bert parks in a white zone at the airport as Peter pulls in behind them. When the plane disembarks, Duster gets loose, sending a stampede of screaming passengers into the terminal. A security guard panics and pulls the fire alarm. To avoid getting into trouble, the children slide down a luggage chute and sprint outside. Meanwhile, Duke cracks a safe, but before he can grab any the money, the alarm sounds causing Bert to knock the safe’s door shut. Fearing detection, the criminals peel off their maintenance uniforms and run outside in time to see their illegally parked Volkswagen towed away. They jump into a cab but find Tracy and Jay already there. Duke orders the children out, but Tracy looks into their bag, finds the burglary tools, and threatens to turn them in. As Duke orders the cab driver to go, J. W. Osborne commands Peter to follow. When the cab stops in front of Bert and Duke’s apartment building, Jameson asks if he should retrieve the children, but Osborne wants to see what happens. Back at the airport, two police detectives, Sgt. Turner and Sgt. Longnecker, are told that the only clues left by the safecrackers are two pieces of white adhesive tape. Discovering that nothing was actually stolen, Turner recognizes the modus operandi of a talented but unlucky safecracker he has been trying to catch for five years. Across town, outside the crook’s apartment building, Tracy tells Duke that she and Jay are runaways. Fearing that someone is looking for the children, Duke tells them to leave, but Tracy pretends she has asthma, which is worsened by the night air, and Duke permits them to stay for one night. Believing that the children are in no danger, Osborne leaves Peter to watch the apartment and drives home with Jameson. Inside their apartment, Bert and Duke find Big Joe, a loan shark, and his henchman, Freddie, who demand repayment of a $9000 within seventy-two hours. When Big Joe asks about the children, Duke introduces them as his niece and nephew. Seeing an opportunity to get money to fly to Hong Kong, Tracy tells everyone she sent a $100,000 ransom note to her grandfather. Although Duke refuses to be part of a kidnapping plot, Tracy reminds him of Big Joe’s threat and he agrees. However, Osborne realizes the ransom is a scheme by Tracy. Wanting Bert and Duke to watch the kids for the weekend, Osborne leaves a note at the drop off point saying he needs more time to gather the money. Tracy decides Osborne is stalling and calls the police to reports the kidnapping. Turner and Longnecker are assigned to the case and tell Osborne, they tell him not to respond until they tell him to. When Duke sees a press conference with Turner on television, he realizes this is the detective who has been chasing him for years. Later, Duke mails a second ransom note, this time for the reduced rate of $75,000, and returns to find Bert on the floor as the result of a judo lesson from Jay. Bert reports that the children went to buy liniment for his back and they hear a knock at the door. A policeman notifies them that he has the children, so Duke and Bert head to the station where Tracy and Jay are being held for having a skunk without a license. As Duke pays the fine, Sgt. Turner arrives, but Bert and Duke quickly flee with the children. Later, Duke comes home with a new dress for Tracy, who is overjoyed and kisses him on the cheek. Duke then mails yet another ransom, now discounted to $30,000, while Jay booby traps the apartment in case Big Joe comes back. The next day, Osborne gives Sgt. Turner the third note and decides to set a trap at the drop-off point. Unaware of Turner’s plan, Osborne is surprised when Carolyn arrives and demands that her father-in-law pay the ransom. Osborne retrieves the money from his walk-in safe, but accidently leaves it open. At the dockside drop-off point, Turner and Longnecker await in a Rolls Royce with Turner wearing a latex mask to look like Osborne. Bert and Duke arrive in a small convertible, wearing their own masks. As Duke approaches “Osborne,” the real Osborne and Carolyn show up. Duke and Bert escape, but not before Carolyn leaps into the backseat of their convertible. Longnecker radios for the squad cars to cut them off, but Bert maneuvers away as police cruisers smash into cotton bales and skid on bananas. As Turner and Longnecker give chase. Duke berates Carolyn for being a bad mother, noting that he and Bert just spent three days with her children while she has been absent. The chase ends when Bert propels their car onto a barge and Longnecker drives off a pier. Meanwhile, Big Joe spots Tracy and Jay’s picture in the newspaper and decides to kidnap them himself. He and Freddie go to the apartment to force Tracy to write a $1 million dollar ransom note. However, Jay triggers his booby traps and Joe and Freddie find themselves hanging upside down from the ceiling. As Jay and Tracy sneak out the back with Duke’s safecracking tools, Osborne and Peter arrive, trigger more traps and find themselves hanging near Big Joe. Jay searches for his skunk, Duster, then finds his pet when a screaming crowd runs out of a restaurant. Longnecker hears the police report about two children and a skunk and goes to Duke’s apartment, where he triggers another trap and hangs beside the other men. Tracy and Jay hitch a ride to Osborne’s mansion to borrow money and find the safe opened. When they hear someone coming, they climb into the safe, but Jameson enters and shuts them inside. Soon, Duke, Bert and Carolyn arrive at the mansion, followed by Turner. Carolyn tells Turner the children were spotted nearby, but Jameson assures them no one is home. However, Duster sprays Osborne’s dog and Duke realizes that Jay must be near. When they hear the children in the safe, Duke estimates they have less than twenty minutes of oxygen and Jameson reports that only Osborne knows the combination. Duke, who is not yet recognized by his adversary, tells Turner that he once worked for a safe company and offers to open it. Turner says only one man could open it, the criminal he has been pursuing for many years. As Duke goes to work, Turner discovers his safecracking tools and realizes Duke’s true identity. Duke opens the safe just as the children run out of air, and Turner tells Duke he was wrong; there are two who can open the safe. Duke agrees, and promises Turner that the other safecracker is permanently retired. The next day, Osborne gives Duke a loan to open a garage and Carolyn announces she is staying in Los Angeles. A space rocket smashes into the chandelier and everyone yells at Jay, but he informs them it was Osborne’s fault. Osborne then takes Jay outside for a judo lesson and throws him into the fountain.