How we cite our quotes: (Act.Line)
Quote #1
Stephen: may I ask how soon you intend to realize that you are a grown-up man, and that I am only a woman? (1.15)
Lady B is playing at needing Stephen's advice. She claims to be "only a woman," but don't be fooled—she's in charge during the whole convo about family finances, and she expects to stay that way.
Quote #2
There may have been some reason for it when the Undershafts could only marry women in their own class, whose sons were not fit to govern great estates. But there could be no excuse for passing over my son. (1.61)
Here, Lady Brit is musing over her husband's power to make decisions for their family—big ones—without her consent. Even though she's making a big show about how it would be unacceptable to have "her son" passed over, ultimately her husband (as convention demands) will make the call.
Quote #3
Barbara: you have had the education of a lady. Please let your father see that; and don't talk like a street girl. (1.181)
Lady Brit seems a bit dismayed by her daughter's behavior upon seeing her father for the first time in years, wanting to make sure Andrew can see that she has brought Barbara up as a "lady." It probably seems old fashioned to readers now, but apparently that was a reasonable thing to be concerned about in turn-of-the-century England.