As Russell Donovan (Bill Bixby) rides into Quake City in 1879, he finds the dusty streets welcoming him like an open frontier, urging him to claim his share of the Wild West. His goal is to set up a casino in New Orleans, but first, he has to retrieve valuables arriving on the next stagecoach, fulfilling a request from his old associate John Wintle. Unbeknownst to Donovan, Wintle has fled, leaving behind three orphaned children: Bobby, Clovis, and Celia Bradley. This unexpected turn of events places the responsibility of caring for the children squarely on Donovan's shoulders.
The stagecoach driver, Magnolia "Dusty" Clydesdale (Susan Clark), informs Donovan that Wintle had been their guardian, and now they are his wards by default. As the townspeople gather, Sheriff Homer McCoy (Harry Morgan) reveals to Donovan that he is legally obligated to look after the children unless someone else steps in. However, the Bradleys are a handful; they cause chaos throughout Quake City, taking a ride in an old mine cart and creating rampage, leading to demands for compensation that further drain Donovan’s funds, jeopardizing his plans for New Orleans.
At the same time, a menacing new threat arises in the form of the Hashknife Outfit, composed of the bumbling yet menacing Amos Tucker (Tim Conway) and Theodore Ogelvie (Don Knotts). These two were once part of the fearsome Stillwell Gang until they were ousted by their boss, Frank Stillwell (Slim Pickens), for debilitating him. Intent on swindling Donovan of his valuables, their series of heist attempts comically crumble, but they remain a persistent threat. Amidst this lawless landscape, Donovan must balance the chaos caused by the Bradley siblings and fend off the corrupt intentions of the Hashknife Outfit.
As the Bradleys—Bobby, Clovis, and Celia—look to support their guardian, they stumble upon a surprising encounter at the hideout of Amos and Theodore, mistakenly believed to be allies. In a twist of fate, they discover a significant gold nugget buried deep in the mine. The news of this discovery spreads rapidly, leading many to express interest in the children as means to access the treasure. Concerned that these new "friends" might exploit the kids, Donovan enacts a quick plan, marrying Dusty, thereby ensuring custody of his newfound wards while he makes a trip to New Orleans. However, complications arise when Wintle unexpectedly returns, determined to reclaim his 'wards' and possess a court order demanding their return.
Meanwhile, Amos and Theodore devise a scheme to steal the Bradleys' gold from the local bank, planning their grand escape to Mexico. Their comedically flawed attempt—complete with a clumsy rappelling act—results in their capture, leading Sheriff McCoy to hand down punishment to discourage further lawlessness. Frustrated and outwitted, they retreat to their hideout once more, creating an aura of mischief that lingers throughout the town.
With the inevitable chaos brewing, the Stillwell Gang, led by Frank, concocts a scheme to seize the gold. Disguised as a clergyman, he infiltrates the circle of Colonel T.R. Clydesdale (David Wayne), exploiting trust to learn key details regarding the gold's transportation. The bond between the Bradley siblings and Donovan grows stronger, leading them to inform Amos and Theodore that they are willing to let them in on their treasure plans. With Donovan's guardianship uncertain, the Stillwell Gang sees an opening; if the prized nugget goes missing, Wintle’s interest in the children will dissipate, allowing him to abandon his claims.
In a gripping culmination of events, the Stillwell Gang enacts a brazen daytime bank heist to acquire the nugget. In a twist of chaos, the Bradley siblings join forces with the Hashknife Outfit to orchestrate their own robbery. Chaos reigns as Amos and Theodore confront Frank, narrowly evading calamity when his gang's henchmen engage in a shootout with local law enforcement.
When Frank’s plans fall apart, he abandons the gold and kidnaps Celia. In a heroic act, Donovan, accompanied by Dusty, intervenes, rescuing her and realizing their deep love for one another amidst the pandemonium—culminating in a heartfelt embrace.
As the town descends into further chaos and confusion, Amos and Theodore find refuge in the bank's vault only to inadvertently trigger dynamite, collapsing the structure and scattering the gold across the town. Ultimately, with Wintle relinquishing his claim over the children and his guardianship, Donovan seizes the opportunity to collect Stillwell's bounty to fund his casino. However, he opts instead to invest in a ranch for himself, Dusty, and their newfound family—the Bradley children.
As they embark on their journey to their new home, the reformed duo of Amos and Theodore arrives at Donovan's side, seeking work as farmhands, which Donovan happily accepts, bringing a sense of closure to their whimsical adventures.
