The spill should never be left to dry. The General Instruction of the Roman Missal states: “If any of the precious blood spills, the area should be washed and the water poured into the sacrarium” (280).
All ministers of Holy Communion should show the greatest reverence for the Most Holy Eucharist by their demeanor, their attire, and the manner in which they handle the consecrated bread or wine. Should there be any mishap—as when, for example, the consecrated wine is spilled from the chalice—then the affected area . . . should be washed and the water poured into the sacrarium. (Norms for the Distribution and Reception of Holy Communion Under Both Kinds in the Dioceses of the United States of America, 29)
To lessen your anxiety, perhaps this is a good time to revisit with your children the proper way to receive the chalice at Mass. However, young children and anyone who suffers from tremors need not—and if possible should not—receive from the chalice.