Several conflicts make the relationship between Stella and Blanche clash horribly to the point of having to take sides, and even having to betray one's own blood.
Stella and Blanche grew up as two rich Southern Belles during a care-free time and, evidently, with very little structure and discipline from their parents. This is evident in Stella's elopement from her home at a very young age with a brute, drunkard former soldier which is Stan Kowalski. The little influence that Blanche may have had over Stella's choices clearly denotes that there had already been a huge disconnect in the relationship between the two sisters.
After Stella went away she basically became the family's lost cause. Hence, it was Blanche who had to put up with the changes that took place at Belle Reeve; to witness the slow deaths of her parents, the loss of their plantation home, and then the tragic end of her own marriage.
Meanwhile, Stella slummed down happily with Stan. Living in a small apartment, she accepted his drinking, his physical abuse, and his rough ways merely because she was sexually attached to him first and foremost. We find in Stella a very unsympathetic character who seems to enjoy her role as a victim of the battered woman syndrome.
It is not until the sisters meet again, which is where the play begins, that the two had finally meet and catch-up. Still then, we find their conversations superficial; every time there is the topic of Belle Reeve, or anything tragic, the two sisters cannot come to a point of opening up completely and showing their true emotions. They just revert back to the old roles of Blanche being the older, protective sister and Stella being the young, innocent one: none of the sisters, however, is what they appear to be.
Therefore, upon Blanche's arrival another "show" begins to play in the Kowalski home: she will play the virtuous, rich diva while Stella would blindly accept everything that Blanche says.None of this was making any sense to Stanley and, after many demonstrations of dislike, hatred, and disbelief, Stanley forces himself upon Blanche as a last act of humiliation against her. How would Stella react? the audience asks. But Stella's reaction of disbelief and support for Stanley comes to no surprise.
We already discussed how Stella is so attached to Stanley's physical prowess that she is willing to accept anything coming from him. This reason, as well as because of the superficial nature of her relationship with her own sister, is what leads Stella to prefer to believe in Stanley, than to even consider her sister's claims of rape.
Moreover, we have also seen how Stella has a very aloof and careless personality. She has never had to suffer and even her current issues with Stanley are problems that she has elected to create for herself. Stella is as empty-headed and irresponsible as the family who raised her. Even though she does love her sister, and she wishes that things were different, the fact remains that Stella is powerless, and still too dependent on Stanley to stand up for herself and for what is correct. As a result, she commits the ultimate act of betrayal by sending her own sister to a mental institution rather than to severe ties with her husband and trying to make life better for the two of them. Blood is not thicker than water in the case of Stella and Blanche.