One example of an object or item that helps to establish the world of the Sycamore/ Vanderhof home would be Grandpa's snakes. They embody that spirit of unconventionality that resides at the very base of the family. The primary reason why the family is perceived as "off" is because of its unconventional nature. Grandpa's snakes are representative of that. They are elements that he cares for and could care less what others, such as Gay or Wilbur Henderson, think of them. Grandpa's essence is to find happiness for himself and the snakes represents that.
I think that another symbol that captures the essence of the Sycamore/ Vanderhof home would be the fireworks in the basement. It is not merely that the fireworks cap off the calamity that is Act II, but they represent something that cannot be contained or constrained. The fundamental argument between Grandpa and Mr. Kirby resides in the collision to live life in accordance to the expectations of others or in accordance to one's own subjectivity:
KIRBY: A man can't give up his business.
GRANDPA: Why not? You've got all the money you need. You can't take it with you.
The fireworks represent something of beauty and of a creative life force, an element towards which Alice remarks,"It's the most beautiful red fire in the world..." The fireworks embody the force of creativity and life that others might not understand. People like Mr. Kirby won't understand such intrinsic worth. However, it is their spirit of vitality that causes one to pursue them and embrace them. It makes sense that at the point the house is run with government agents, who are forces of conformity, the fireworks explode. This embodies how they cannot be controlled or contained. The only element from them that cannot be embraced is the very idea that only their beauty and intrinsic worth can be taken from them. In this regard, the fireworks come to represent the world of the Sycamore/ Vanderhof home.