To what extent do violence and softness exert influence in the play?
You are perfectly correct in thinking that violence and softness, or violence versus softness, are important to Tennessee Williams' A Streetcar Named Desire. The primary conflict is between Blanche DuBois and Stanley Kowalski. The conflict is over Stella, who is the "MacGuffin" or "bone of contention." Blanche is the protagonist and Stanley, although he is much bigger and stronger than Blanche, is the antagonist. Stanley is on the defensive. Blanche dislikes him because he is uncouth and lower-class. She tries to turn Stella against him and seems to be trying to break up their marriage, in spite of the fact that Stella is expecting a baby.
Stanley is brutal and violent. Blanche pretends to be soft, sweet, gentle, refined, sentimental, idealistic. Significantly, Blanche has been an English teacher. She undoubtedly favors romantic poetry by such sentimental authors as Tennyson. She was married to a sentimental young man who wrote poetry. When she comes up against Stanley Kowalski, her attitudinizing is ineffectual. He is everything she is not. She has been said to be a symbol of the old South, while Stanley has been seen as a representative of the new dog-eat-dog South. He is not only animalistic, but he gets sweaty and greasy, drunk and disorderly. Blanche has a hard time maintaining her defense of dainty femininity against his brutal realism and candor. She amuses him. She despises him--but he despises her even more.
A Streetcar Named Desire is all about a contest between realism and idealism, between violence and softness, between masculinity and femininity. If Blanche had been as pure as she pretended to be, she might have had a better chance. But Stanley sees right through her. He finds out that her refinement is corrupt. He may be brutal but he is more moral and wholesome than she is. He may be ignorant, but he sees the truth. She may be educated, but she lives in a world of fantasy.
In Scene Nine she tells Mitch:
I don't want realism. I want magic! [Mitch laughs] Yes, yes, magic! I try to give that to people. I misrepresent things to them. I don't tell truth. I tell what ought to be truth. And if that is sinful, then let me be damned for it!--Don't turn the light on!
Her world is fragile and easily shattered--and Stanley Kowalski shatters it to pieces when she makes the mistake of becoming his adversary. At first she thinks it should be easy to defeat Stanley by making him look like a savage beast in contrast to her own refinement and sensitivity. But she finds out that he is much more subtle and resourceful than he appears on the surface. It is people like Stanley Kowalski who will prevail in the new South, and people like Blanche DuBois who will be trodden down.
It is interesting to see how William Faulkner describes Alfred, Lord Tennyson, who must be one of Blanche's favorite poets as well as a favorite of Faulkner's character Reverend Hightower in the great novel Light in August.
One wall of the study is lined with books. He pauses before them, seeking, until he finds the one which he wants. It is Tennyson. It is dogeared. He has had it ever since the seminary. He sits beneath the lamp and opens it. It does not take long. Soon the fine galloping language, the gutless swooning full of sapless trees and dehydrated lusts begins to swim smooth and swift and peaceful. It is better than praying without having to bother to think aloud. It is like listening in a cathedral to a eunuch chanting in a language which he does not even need to not understand.