If a kitchen sink is where you clean up after nourishing yourself or your family, in a dream it might represent "cleaning up after" yourself or family—especially taking responsibility for its past decisions, direction, and actions—and "cleaning up" any "messes" that have occurred
Responsibility for the mental, emotional, or spiritual nourishment of yourself or your family
A kitchen sink with dirty dishes stacked up can represent a catch-all—someone or something who takes on any and all problems from other people, or someone who has trouble saying no.