The Premier (meaning the Prime Minister of their province) is coming to a nearby town, and pretty much all the adults in Avonlea go to see him speak. Marilla goes, leaving Anne alone with Matthew in the evening.
Anne and Matthew have a good chat about how geometry's hard, and about politics. Matthew says he's a Conservative (a party that was for political economics and ties to England) and Anne decides she's a Conservative by association. She's glad, because Gilbert's a Grit (a party for democratic reform and free trade with the U.S.)
Diana runs into the house suddenly, crying that her sister Minnie May has bad croup. Her parents are away, the girl (Mary Jo) who is supposed to take care of her doesn't know what to do, and the doctor is probably out of town seeing the Premier.
Matthew leaves to get the doctor and Anne takes charge of Minnie May's care. She used to care for three twins, remember? She's got this.
Minnie May is very sick—croup involves a high fever and closes up the vocal chords, so she's also having trouble breathing. Anne uses ipecac (which used to treat coughs and is now mostly used to induce vomiting) to treat her, several times that night.
The doctor arrives very late (as most doctors were at the Premier talk), when Minnie May has improved. Anne explains to him what went down, and how she was scared Minnie May would choke to death before her fever broke.
When the Barry parents return, the doctor tells them Anne saved their child's life.
The next afternoon, when Anne wakes up, Marilla tells her that Mrs. Barry had visited and apologized.
Anne runs to Diana's house and tells Marilla about it afterward: Mrs. Barry had apologized and cried, and then included Anne in an elegant tea using their best china set. Most importantly, Anne and Diana are back to being friends.