Character Analysis
Doris is Neil's cousin. Her family got rich and moved to the suburbs several years ago. We don't know a lot about her, except that she looks down on Neil because his family has less money than hers. It is Doris who invites Neil (once a year, apparently) to the Green Lane Country Club, where he meets Brenda. So, in terms of a plot device she's important, though her role could easily have been omitted or filled by another. We are told several times that she's "always reading War and Peace" (1.47), which is Leo Tolstoy's epic novel featuring the French Invasion of Russia by Napoleon. Perhaps this is a comment on Neil's "invasion" of the Patimkin household, and his framing of his summer adventure as an epic battle where the city and the suburbs face off for his soul.
When Doris agrees to "watch Brenda's glasses" (2.9) so Neil can swim with Brenda, she says:
"Well, for God's sake […], I'm not going to hold them. Put them down. I'm not her slave." (2.12)
Doesn't seem like much, but suddenly we see Neil as others might see him—as a dude totally smitten with Brenda. It's like he's holding the glasses to somehow seem useful to her. This makes us see how young and nervous he is, in spite of his bravado and bluster. So, Doris is more about highlighting certain aspects of Neil than she is a fully drawn character.