When she visited her daughter, Azma did not have a good trip due to not requesting an aisle seat. She was impatient to see the Palace and Yzma as Empress.
Previously, Yzma had told Amza that she had killed Kuzco and taken over the kingdom. After learning that her mother would be coming to visit, she (in disguise as Principal Amzy) asked Kuzco for a favor for her "friend": would Kuzco let her "friend" pretend to be Empress in order to prevent her from being embarassed when the truth was discovered. Kuzco declined.
Yzma was angry but knew that at some point Kuzco would need a favor and she would be waiting. Later that day, Kuzco needed a way out of a pre-arranged marriage. Being Empress was her condition, which Kuzco was able to renegotiate to being only for a day instead of permanent. Her first act as temporary Empress was to have Kronk bring her mother to see her and then to gloat about her new status. Yzma's time as Empress ended when the potion used to change Kuzco's bride-to-be wore off.
Relationship with her daughter
Azma appears to be disappointed in Yzma and has referred to her as a "prune face wannabe". Either her high expectations of Yzma or Yzma's need to prove her mother wrong prompted Yzma to lie about her achievements. Surprisingly, Azma had nothing to say when Yzma was dethroned.
The name "Azma" is a play on the word Asthma, a disease that includes wheezing and coughing, amongst other symptoms. Azma communicates through wheezes in her old age.