The Griffin family plans a vacation to visit Lois' wealthy parents, much to the chagrin of Peter, as his father-in-law Carter Pewterschmidtdislikes him intensely. Meanwhile, Brian's sex drive seems unusually strong lately, causing him to feel stressed out, especially after sniffing the rear-end of an attractive dog at the park. Peter and Lois are oblivious to Brian's state until they walk in on him masturbating in the bathroom. Lois insists it's natural, and suggests that Brian take time off and accompany the family on their road trip. Though he initially declines, Brian joins the Griffins after he learns that if he stays a show entitled World's Sluttiest Dogs will play.
After arriving, Brian is introduced to Carter's greyhound, Seabreeze, who Brian finds attractive. Peter joins an annoyed Carter in a poker match, and helps him win CNN from Ted Turner, thus earning the respect of his father-in-law. Later, Carter and Peter, along with Carter's other poker buddies, Michael Eisner and Bill Gates go out smashing mailboxes to have some "extra fun."
Not long after, the cordiality between Peter and Carter is ruined when during a greyhound race involving Seabreeze, Brian suddenly leaps onto the racetrack, runs to Seabreeze and engages her in sexual intercourse, causing her to lose. Seabreeze then ends up pregnant, and Brian is immediately blamed. Scolding that his relationship with Carter is ruined because of that, Peter swears to never speak with Brian again and goes to incredible lengths to ignore him, such as enclosing himself in a massive plastic bubble (which backfires when Peter farts, causing him to pass out from the stench). Determining to take responsibility, Brian offers to raise the puppies himself, but Carter disapproves, so Brian elopes with Seabreeze and they run away together in hopes to raise the puppies together.
With help from Eisner and Gates, Seabreeze and Brian are tracked down to a motel room they were hiding at. After the custody case soon after goes to court, Carter and his lawyers bring up sordid details of Brian's past and personality to destroy his chances of gaining custody. Just as it appears that Brian may lose, Peter lets go of his hatred towards him and insists that Brian would be a good father (presumably out of revenge against Carter for years of abuse he inflicted on him), and he proves it by having Brian demonstrating his extensive knowledge of the Griffin children. The judge is convinced Brian would make a good father, and awards him custody, but insists that Brian must be neutered in order prevent another similar incident from happening.
Just as Brian was about to go under the knife, he, Lois, and Peter discover that when the puppies are born, they do not resemble Brian; instead, they resemble Ted Turner. Realizing that Turner impregnated Seabreeze in revenge of losing the poker match, the angry and humiliated Carter calls Seabreeze a whore and abandons her on the spot. Brian, realizing that he is not the father, opts out of the surgery, and the three leave to go home. Peter ends the episode by confessing that he thought dogs laid eggs.