In these lines, we hear that Kitty is constantly coughing, which drives her mother crazy. She wants her to stop, and argues that she is getting on her nerves:
"Stop coughing, Kitty. Please! You're getting on my nerves."
To this statement, Kitty's father replies that "Kitty has no discretion in her coughs."
This is an example of sarcasm, used by Kitty's father to make fun of Kitty's mother. He knows that no one can "time" their coughs to someone else's convenience. However, the statement is not understood by Kitty's mother. Sarcasm refers to the use of a witty and sharp remark that uses irony to show contempt. In this example, it is clear that the father feels some contempt for the mother, which is emphasized by the fact that she does not understand the ironic effect of his words.