This phase II trial studies the side effects and best dose of total-body irradiation when given together with fludarabine phosphate followed by a donor peripheral stem cell transplant in treating patients with myelodysplastic syndromes (MDS) or myeloproliferative disorders (MPD). Giving low doses of chemotherapy, such as fludarabine phosphate, and total-body irradiation before a donor peripheral blood stem cell transplant helps stop the growth of cancer cells. Giving chemotherapy or radiation therapy before or after transplant also stops 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.