The Usher family story is one of the best unwritten plot lines Poe has ever devised. The subtle mention he makes in the opening descriptive passages allude to a family built upon corruption and incest. The narrator makes the supposition that the family's "direct line of descent" is the cause for his friend Roderick's troubling mental condition.
As readers, we must wonder at what came before - what were Roderick and Madeleine as children? What were their parents like? A prequel in the making!
In a more tangible way, Poe uses the family dynamics as a source of foreshadowing and conflict. The narrator has come to see Roderick because he is "unsettled". Roderick's internal conflict is connected to his sister's external state. She is ill, so ill that the doctor's cannot diagnose her and have asserted her condition is terminal. She wanders about the house, not socializing, existing and not existing. Roderick is visible troubled. It isn't until she dies and is entombed that Roderick begins to improve.
All seems well for a few days, but then Roderick begins to deteriorate. The resurrgence of his internal conflict is forshadowing the return of Madeleine. Upon her return, he is conquered by his anxiety, and is "bourne to the ground a corpse". The suspense in this story is intertwined with the dynamics of the Usher family.
I think a better question would be, how do family dynamics not impact this story, especially when considering Roderick and his twin sister Madeline. At one point, Roderick even says that he is in the grips of a, "constitutional and family evil." Roderick believes that the house is responsible for his depression and Madeline's illness. The house represents years and years of his family that have lived in it. THe narrator tells us in the beginning of the story that the Usher family partook in a close familial relationship, and a lot of inbreeding. In fact, Madeline and Roderick are the last of the family line. In a way it seems like the house, and whatever spririts are trying to get rid of the family (both in death and in property as the house collapses).