Combination Chemotherapy, Donor Stem Cell Transplant, Tacrolimus, Mycophenolate Mofetil, and Cyclophosphamide in Treating Patients With Hematologic Cancer

DISEASE CHARACTERISTICS: * Diagnosis of one of the following high-risk hematologic malignancies: * Chronic myelogenous leukemia meeting one of the following criteria: * Disease in chronic phase and resistant to available tyrosine kinase inhibitors * Disease in accelerated phase * Disease with blast crisis that has entered into a second chronic phase after induction chemotherapy * Acute myelogenous leukemia meeting the following criteria: * Marrow blasts \< 5% but persistence of minimal residual disease by flow cytometry, cytogenetics, or FISH * Must meet one of the following criteria: * Disease in second or subsequent complete remission * Primary induction chemotherapy failure with disease subsequently entering complete remission * Disease in first complete remission with poor-risk cytogenetics or arising from preceding hematological disease * Myelodysplastic syndrome meeting at least one of the following criteria: * Treatment-related * Monosomy 7 or complex cytogenetics * International prognostic scoring system score ≥ 1.5 * Chronic myelomonocytic leukemia * Acute lymphocytic leukemia or lymphoblastic lymphoma meeting the following criteria: * Marrow blasts \< 5% but persistence of minimal residual disease by flow cytometry, cytogenetics, or FISH * Must meet one of the following criteria: * Disease in second or subsequent complete remission * Acute lymphocytic leukemia with poor-risk karyotype \[e.g., t(9;22) or bcr-abl fusion, t(4;11), or other MLL translocation\] and in first complete remission * Chronic lymphocytic leukemia or prolymphocytic leukemia meeting both of the following criteria: * Previously treated disease that has either relapsed or failed to respond adequately to conventional-dose therapy including purine analogs * In the opinion of the transplant physician, unlikely to benefit from reduced intensity transplantation due to the presence of one or more high-risk features (i.e., bulky tumor masses, B symptoms, and/or inadequate response to salvage chemotherapy) * Hodgkin or non-Hodgkin lymphoma (including low-grade, mantle cell, and intermediate-grade/diffuse disease) meeting the following criteria: * Previously treated disease that has either relapsed or failed to respond adequately to conventional-dose therapy or autologous transplantation * In the opinion of the transplant physician, unlikely to benefit from reduced intensity transplantation due to the presence of one or more high-risk features (i.e., bulky tumor masses, B symptoms, and/or inadequate response to salvage chemotherapy) NOTE: A new classification scheme for adult non-Hodgkin lymphoma has been adopted by PDQ. The terminology of "indolent" or "aggressive" lymphoma will replace the former terminology of "low", "intermediate", or "high" grade lymphoma. However, this protocol uses the former terminology. * No available matched related or unrelated donor OR a matched related or unrelated donor will not be available in the time frame necessary to perform a transplant * Availability of a first-degree relative (parent, child, sibling) matched at 3/6-5/6 loci (HLA-A, -B, -DR) * Donor must be willing to donate mobilized peripheral blood stem cells * No positive HLA crossmatch in the host-vs-graft direction or high titer donor-specific antibodies PATIENT CHARACTERISTICS: * Karnofsky performance status 70-100% * Bilirubin \< 2 mg/dL (unless due to hemolysis, Gilbert syndrome, or primary malignancy) * Creatinine \< 2 mg/dL OR creatinine clearance ≥ 40 mL/min * Not pregnant * Fertile patients must use effective contraception * LVEF (Left ventriculr ejection fraction) ≥ 45% * FEV\_1 and forced vital capacity ≥ 50% predicted * No HIV positivity * No debilitating medical or psychiatric illness that would preclude giving informed consent or receiving optimal treatment and follow-up PRIOR CONCURRENT THERAPY: * See Disease Characteristics * No immunosuppressive agents ≤ 24 hours after completion of post-transplant cyclophosphamide (including steroids as antiemetics)