This pilot trial studies decitabine, donor natural killer cells, and aldesleukin in treating patients with acute myeloid leukemia that has come back after previous treatment (relapsed) or has not responded to previous treatment (refractory). Drugs used in chemotherapy, such as decitabine, work in different ways to stop the growth of cancer cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving donor natural killer cells after decitabine may boost the patient's immune system by helping it see the remaining cancer cells as not belonging in the patient's body and causing it to destroy them (called graft-versus-tumor effect). Aldesleukin may stimulate natural killer cells to kill acute myeloid leukemia cells. Giving decitabine, donor natural killer cells, and aldesleukin may be a better treatment for acute myeloid leukemia.