Since Blanche's family fell from the upper crust of Southern society, her nostalgia over times gone by has turned her into a money-hungry and calculating woman who uses sex to attract possible rich suitors, but without success. She is very desperate for money, especially since she has none, and her tricks are not working anymore.
In that scene when her sister offered her money, she basically exploded in a rant of how low her sister has fallen and what a low life her sister's husband is. He heard the whole thing, but he pretended not to have heard her. Which, in turn, added to the fuel of anger that he was harboring towards Blanche.