Homer participates in a KBBL-sponsored drinking contest at P.J. O'Harrigan's, an Irish pub, and wins the trophy and title of "Sir Drinks-A-Lot". Once sober, Marge reminds Homer of his promise to spend one Saturday a month with the children. Much to Homer's chagrin, Bart traded his turn to choose with Lisa for her dessert, and Lisa suggests that the family go to the traveling Smithsonian Institution exhibit. Homer attempts to punish Bart for giving his turn to Lisa by forbidding him to have any dessert, but this backfires when Bart makes another deal to give his turn to Lisa in exchange for her dessert again, much to Homer's discomfort. They arrive at the exhibit, which is sponsored by a cell phone company called OmniTouch, has Abraham Lincoln's hat, Fonzie's jacket, Archie Bunker's chair, and the Bill of Rights, which is ruined when Homer reads it with chocolate-covered hands. In an attempt to lick it clean he licks off the section that forbids cruel and unusual punishment. Homer is unable to pay the $10,000 repair bill and so Omnitouch installs a cellular transmitter on the roof of his house, with the control equipment in Lisa's room. Lisa moves in with Bart, but she is overwhelmed when Bart has made up rules and noises distract her from her homework.
When Lisa develops stomach aches, she visits Dr. Hibbert, who suggests he could prescribe 'harsh Antacids' but says herbal tea could also work. Lisa wants the tea but Homer, scoffs at the tea and demands the antacids. While leaving the office Lisa has had enough and snaps at her father for belittling everything she believes in. When Lisa sees how she upset him, she says that they are just too different and will eventually drift apart. To make things up to her, Homer takes her to a local New Age store which introduces Homer and Lisa to water-filled sensory deprivation tanks, where they experience their own spiritual journey. On her journey, Lisa sees herself from Homer's perspective, reprimanding him for snoring during a ballet recital. Lisa realizes that despite his boorish personality, Homer loves Lisa enough to take her to events and places that he does not personally like just so she can be happy. Meanwhile, a pair of repo men start to clean out the store despite the lease not being up for months, taking the tank that Homer is in. Homer's "journey" becomes a real one, as his tank falls out of the back of the van. Mistaken by the Flanders' as a coffin, they bury him, only for the tank to fall through the soil and into a pipe where it is washed up onto the beach. Chief Wiggum finds it and returns it to the store. Lisa decides to go and do something they both enjoy. But they end up at a demolition derby together, even though Homer is the only fan.
Meanwhile, Maggie's baby monitor receives transmission from the cellular tower. Rather than report this to Omnitouch, Marge becomes obsessed with eavesdropping on private calls. Eventually Bart and Milhouse play a prank on Marge by making her think that an escaped convict was attempting to break into the house. Marge smashes the baby monitor on Milhouse's head when he opens the door, knocking him out, but when Marge scolds Bart for the prank, he rebukes that it was a fair punishment for eavesdropping, to which Marge reluctantly agrees.