This phase I trial studies the side effects and best dose of iodine I 131 monoclonal antibody BC8 when given together with fludarabine phosphate and low-dose total-body irradiation followed by donor stem cell transplant and immunosuppression therapy in treating older patients with acute myeloid leukemia or high-risk myelodysplastic syndromes that cannot be controlled with treatment. Radiolabeled monoclonal antibodies, such as iodine I 131 monoclonal antibody BC8, can find cancer cells and carry cancer-killing substances to them. Giving chemotherapy, such as fludarabine phosphate, and total-body irradiation before a donor peripheral blood stem cell transplant helps stop the growth of cancer or abnormal cells. It may also stop the patient's immune system from rejecting the donor's stem cells. When the healthy stem cells from a donor are infused into the patient they may help the patient's bone marrow make stem cells, red blood cells, white blood cells, and platelets. The donated stem cells may also replace the patient's immune cells and help destroy any remaining cancer cells. Sometimes the transplanted cells from a donor can also make an immune response against the body's normal cells. Giving radiolabeled monoclonal antibody therapy together with fludarabine phosphate and total-body irradiation before the transplant together with cyclosporine and mycophenolate mofetil after the transplant may stop this from happening.