This phase I trial studies pretargeted radioimmunotherapy and donor peripheral blood stem cell transplant employing fludarabine phosphate and total-body irradiation (TBI) to treat patients with high-risk acute myeloid leukemia, acute lymphoblastic leukemia, or myelodysplastic syndrome. Giving chemotherapy drugs, such as fludarabine phosphate, and TBI before a donor peripheral blood stem cell transplant helps stop the patient's immune system from rejecting the donor's stem cells. Radiolabeled monoclonal antibodies can be combined with fludarabine phosphate and TBI to find cancer cells and kill them without harming normal cells. Pretargeted radioimmunotherapy (PRIT) allows for further improved targeting of tumor cells over standard directly labeled antibodies.