There are three dreams which drive the Younger family in A Raisin in the Sun, two of which seem to work against each other.
Beneatha has a dream of becoming a doctor and finding a way to achieve dignity. It is dignity, above all else, which orients Beneatha's character, her turmoil, her conflicts with George, Asagai, and with her mother. Dignity also, essentially, focuses her dream. Becoming a doctor can be related to the American Dream:
The "American Dream" includes many ideas, but it is primarily the belief that anyone who comes to or is born in America can achieve success through hard work.
This argument is potent especially because Beneatha's goal is unconventional. Despite being an uncommon dream, Beneatha's aim is possible, however, this dream does not interfere with Walter's dream in a significant way, nor does it interfere with the goal which Mama and Ruth share.
Like Beneatha, Walter wants to prove his worth, prove his abilities and strike out on his own. He wants to own a business. This is also highly relatable to the concept of the American Dream. Walter's dream is, in a small but significant way, in conflict with his wife's goals for the family.
Ruth only wants to be comfortable and happy. Walter feels that he cannot be happy without a major change in his professional status. Ruth feels, like Mama, that if they just love and accept one another they can have happiness first and professional changes can come when they will.