Grampa Simpson falls in love with Marge's mother, Jacqueline, but Mr. Burns whisks her away from him. Grampa is broken hearted when learning Jackie is going to marry Burns.
The episode starts off with the Simpson family celebrating Maggie's first birthday--besides Homer, Marge, Bart, Lisa and, of course, Maggie, the other people at the party consist of Homer's dad, Abe (who initially stops at the wrong house), and Marge's sisters, Patty and Selma, and their mother, Jackie.
During the party, Abe and Jackie end up bonding and later on, Marge points out to Homer that both her mother and Homer's father seem kind of lonely, so Marge suggests setting them up on a date. Abe and Jackie end up falling in love, but while Marge is happy for them, Homer's against the relationship, pointing out that if Abe and Jackie end up getting married, it would make him and Marge stepsiblings. Abe and Jackie's relationship goes well until when on a night on the town, Jackie goes dancing with Mr. Burns, whom she finds to be more dashing.
Meanwhile, Bart hears about an Itchy & Scratchy animation cel which costs $350 when he is watching a TV shopping channel. He buys one with one of Homer's credit cards. He then endures a long and painful wait for its delivery on delivery day (both figuratively and literally, as Bart had to endure punches in the face from irate townspeople for things that Homer did while waiting for the delivery), before acquiring it, which to his dismay was just Scratchy's severed arm. Burns declares that he is in love with Mrs. Bouvier, against Marge's interests. Bart gets $350 from Burns to pay Homer back (which Homer, not listening to Bart explicitly saying it was to pay him back, thinks Bart is just giving him free money and runs off to spend it foolishly).
On the day of the wedding, Mr. Burns and Jacqueline attempt to marry. Only minutes before Mrs. Bouvier becomes Mrs. Montgomery Burns, in a scene similar to one from The Graduate, Abe crashes the ceremony by arguing that Mrs. Bouvier shouldn't get married to Burns. In the end, Jackie chooses not to marry Burns or Abe, which is good enough for Abe--they hop on a bus and look anxious about their future. This likely leaves Mr. Burns heartbroken.