It's Maggie's first birthday, and the rest of the family invites Abe, Patty and Selma, and Jackie Bouvier. At the party, Abe is feeling lonely, and when he is bored, Marge suggests she set up a date for him with her mother--Marge seems fine with Abe dating her mother while Homer's against it, mostly because if Abe and Jackie get married, it would Homer 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. Mr. Burns declares that he is in love with Mrs. Bouvier, against Marge's interests. Bart gets $350 from Mr. 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).
It is the day of the wedding, and Mr. Burns and Marge's mother 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 should not get married to Mr. Burns. She declares that she does not want to marry either man, and they hop on a bus and look anxious about their future.