In the end, Scarlett has to ask Frank Kennedy to marry him for two reasons. Scarlett could not simply ask Kennedy for money as a matter of social tradition. At the time when she accepts Frank Kennedy's offer of marriage, Scarlett still believed, to an extent, the Southern conditions of honor and tradition for a woman. She recognizes that Frank is fundamentally weak and would not recognize her advances without a marriage, and so Scarlett steals him from Suellen in order to get what she wants. Accordingly, Scarlett could not very well have asked him for money outright. Rather, she was bound to accept his proposition of marriage and then do with him as she needed to as his wife. There is a part of this that is reflective of Scarlett's sibling rivalry and her desire to be superior to her sisters. This is why she covets Frank's money and his position as Suellen's fiancee, resulting in her stealing of him. The combination of desire for something that is not hers, money that will help Tara, and the need to continually be in a position of power are all reasons why Scarlett could not simply ask for money, but rather obtain it in a manner that shows strength.
Scarlett knew that if she asked Frank for money,her sister Suellen would have never agreed. Frank needed to earn money before he got married to Suellen,and Suellen wanted to get married fast. She would not have let the money go to save Tara.