I think that the basis of the conflict in A Streetcar Named Desireis for control. When Blanche enters, a critical choice is forced between Stanley and Blanche. Stella is the one whose decision becomes an ultimatum of sorts. The bitterness is reflected in the antagonism that both Stanley and Blanche have towards both one another and what the other represents. Stella is poised between equally desirable, but ultimately incompatible courses of action.
Both Stanley and Blanche battle for superiority and control. For Blanche, ensuring that Stella place primacy on her over Stanley represents the last vestige of a past that makes sense. Her battle for control operates on both emotional and existential levels. Stanley also views the conflict in terms of ultimatum, when he speaks to Stella about her past without him and her future with him:
"When we first met, me and you, you thought I was common. How right you was, baby. I was common as dirt. You showed me the snapshot of the place with the columns [Belle Reve]. I pulled you down off them columns and how you loved it."
In the end, this becomes the conflict that underscores the drama. Both Stanley and Blanche are competing for their view of the world to be embraced. More importantly, their competition for control seeks to obliterate the other. The result is a condition where no one really wins, but rather one sees a different degree of loss and sadness evident.