In terms of the American Dream, a key to a house can actually act as a very important symbol of the American Dream, as possession of your own property and own living space is something that is part of the American Dream: having your own land, having earned enough to be able to afford a house and owning that house rather than renting can be viewed as the core of the original American Dream and finding success in America.
In terms of examples from literature, the immediate example that comes to mind is from The House in Mango Street, by Sandra Cisneros, which describes the thoughts and feelings of the daughter of a Latino immigrant family as she grows up in a barrio in the United States and copes with the various difficulties and problems that she and her community have as a result of their identity. What Esperanza grows up to want, more than anything, is a house of her own, and in the chapter with the same title, she describes this longing:
Not a flat. Not an apartment in back. Not a man's house. Not a daddy's. A house all my own. With my porch and my pillow, my pretty purple petunias. My books and my stories. My two shoes waiting beside the bed. Nobody to shake a stick at. Nobody's garbage to pick up after.
Clearly here, for Esperanza, part of her American Dream is gaining a key to her own house so that she can have that independence and privacy, and above all, her own personal space, that she clearly desires and craves. The novel ends with Esperanza leaving her community as she sets out to achieve her dream.