This phase II trial studies how well reduced intensity donor peripheral blood stem cell (PBSC) transplant works in treating patients with de novo or secondary acute myeloid leukemia (AML) in remission. Giving low doses of chemotherapy, such as fludarabine phosphate, and total-body irradiation (TBI) before a donor PBSC transplant helps stop the growth of cancer cells. It may also stop the patient's immune system from rejecting the donor's stem cells. The donated stem cells may replace the patient's immune cells and help destroy any remaining cancer cells (graft-versus-tumor effect). Sometimes the transplanted cells from a donor can also make an immune response against the body's normal cells. Giving cyclosporine and mycophenolate mofetil after the transplant may stop this from happening