What is the role of women during 1930's in the south?

There was not one single role for women in any time or place in history.  Things differed to some extent based on the family of the individual woman, whether they were urban or rural, etc.

In general, women's lives in the 1930s were "opening up" a bit, especially early in the decade.  The 1920s had seen a big cultural change that had helped women become more free.  It had become more acceptable for women to do various things in public that they had not been allowed to do before.

Later in the 1930s, the Great Depression changed everyone's lives.  Women had a much harder time then because they more often had to work (if they could find it) to allow their families just to survive.

So -- women were still not equal to men legally or in fact.  But people's atttitudes towards women had loosened up some by the 1930s.