With a novel based on a true story, like Farewell to Manzanar, we should use caution when interpreting actions and objects as symbols. The events in the story really did happen to the author, so it's not as if she was sitting around with her typewriter dreaming up good symbols for the meaning she intended to convey.
Still, the broken china is very meaningful to the plot and could be interpreted as a representation of both the high value and the fragility of human autonomy and dignity.
In Chapter 2, when the government gives Jeanne's family only two days' notice to leave their home on Terminal Island, Jeanne's mother is in a rush to sell her valuable possessions, knowing that she has no way of packing them and keeping track of them as the family is shuffled off to an unknown destination. It's a full set of china, worth at least $200, as Jeanne's narration explains. A dealer offers $15 for it. Jeanne's mother's fury is obvious, and the dealer raises his offer to $17.50. It's at that point that Jeanne's mother starts smashing her own dishes: throwing them onto the floor, fragmenting them into tiny pieces in defiance of the dealer. He flees, but she continues shattering the entire set, silently crying.
The point here is that the china is valuable. It's going to be taken away, regardless of how. And Jeanne's mother refuses to submit to the degradation and humiliation of giving it away for less than a tenth of its real value. Rather than take such a demeaning offer, she'd rather take nothing—she prefers to lose the china on her own terms.
Reading into this scene a bit, then, we can understand that the china is both valuable and fragile. It can be sold; it can be easily broken. The fact that one person would rather break her own china than sell it for almost nothing symbolizes the violent strength of the human spirit and our deep need for autonomy (for control over our own lives). Swept up in the fear surrounding World War II, the US government is quick to impinge on Japanese citizens' human rights, but the breaking of the china is Jeanne's mother's own way of rebelling against that impingement.