Alpha/Beta CD19+ Depleted Haploidentical Transplantation + Zometa for Pediatric Hematologic Malignancies and Solid Tumors

Inclusion Criteria: * Availability of an eligible haploidentical donor * Hematologic malignancy or solid tumor * Patients with more than one malignancy (hematologic or solid tumor) are eligible * Patients with hematologic malignancy must have no HLA identical sibling or suitable unrelated donor OR time needed to find an acceptable unrelated donor match would likely result in disease progression such that the patient may become ineligible for any type of potentially curative transplant * Relapsed or primary therapy-refractory AML with bone marrow blast \< 20% * High-risk refractory or relapsed ALL in patients for whom transplantation is deemed indicated (relapse occurring \< 30 months from diagnosis, patients relapsing after previous allogeneic transplant, relapse after 2nd remission, primary induction failure or hypodiploidy) * Relapsed Hodgkin lymphoma unable to achieve 2nd remission or Very Good Partial Response (VGPR) and therefore ineligible to receive autologous hematopoietic stem cell transplant (auto-HSCT) * Hodgkin lymphoma relapsing after auto-HSCT * Primary refractory or relapsed non-Hodgkin lymphoma unable to achieve 2nd remission or VGPR and therefore ineligible to receive auto-HSCT * Non-Hodgkin lymphoma relapsing after auto-HSCT * Myelodysplastic Syndrome/Myeloproliferative Syndrome Solid Tumor * Patients with solid tumor must have failed or have been ineligible to receive auto-HSCT or if auto-HSCT would not offer \> 20% chance of cure * Neuroblastoma * high risk with relapsed or refractory disease * Soft tissue sarcomas (Rhabdomyosarcoma, Ewing sarcoma, Primitive Neuroectodermal Tumor or other high-risk extracranial solid tumors) * Relapsed or primary refractory metastatic * 1st complete remission, but very high-risk features (i.e., \< 20% survival with conventional therapy) * Osteosarcoma * Failure to achieve Complete Response (CR) following initial therapy * Relapsed with pulmonary or bone metastases and did not achieve a CR with surgery and/or chemotherapy * Karnofsky (patients \> 16 years) or Lansky (patients 16 years or older) performance score of ≥ 60 * Life expectancy of ≥ 3 months * Patient must have fully recovered from acute toxic effects of all prior chemotherapy, immunotherapy, or radiotherapy prior to entering this study * Study enrollment no earlier than 3 months after preceding HSCT * Glomerular Filtration Rate (GFR) ≥ 60 ml/min/1.73m2 * Total bilirubin \< 3 mg/dL * ALT (alanine aminotransferase, SCPT) ≤ 5 x Upper LImit of Normal (ULN) for age * Ejection fraction of \> 40% by Multigated Acquisition Scan (MUGA) or echocardiogram * No evidence of dyspnea at rest * No supplemental oxygen requirement * If measured, carbon monoxide diffusion capacity (DLCO) \>50% * No severe peripheral neuropathy, signs of leukoencephalopathy or active Central Nervous System (CNS) infection * Patients with seizure disorders may be enrolled if seizures are well controlled on anticonvulsant therapy * If of reproductive potential, negative pregnancy test and willing to use effective birth control method * Informed consent from patient or legal guardian (if patient is minor) Inclusion Criteria for Donors: * Donor must be 18 years of age minimum, 65 years of age maximum * Donor must be in good general health as determined by evaluating medical provider * Must meet donor criteria for human cells, tissues, and cellular and tissue-based products per Code of Federal Regulations 21 CFR 1271, subpart C. Specifically: * Donor screening in accordance with 1271.75 indicates that the donor: * Is free from risk factors for, and clinical evidence of, infection due to relevant communicable disease agents and diseases; and * Is free from communicable disease risks associated with xenotransplantation; and * The results of donor testing for relevant communicable disease agents in accordance with 1271.80 and 1271.85 are negative or nonreactive, except as provided in 1271.80(d)(1). * Haploidentical by HLA-typing * Preference will be given to donors who demonstrate KIR incompatibility with recipient HLA class I ligands defined as the donor expressing a KIR gene for which the corresponding HLA class I ligand is not expressed by the recipient. * Negative testing for relevant communicable diseases: * Hepatitis B surface antigen (HBsAg) * Hepatitis B core antibody (Anti-HBc) * Hepatitis C antibody (Anti-HCV) * HIV 1 \& 2 antibody (Anti-HIV-1, 2 plus O) * HTLV I/II antibody (Anti-HTLV I/II) * RPR (Syphilis TP) * CMV (Capture CMV) * MPX for: HepB (HBV-PCR), HepC (HCV-PCR), HIV (HIV-PCR) * NAT for West Nile Virus (WNV-PCR) * T. Cruzi - EIA (Chagas) Exclusion Criteria: * Pregnant or breast-feeding * HIV infection * Heart failure or uncontrolled cardiac rhythm disturbance * Uncontrolled, Serious Active Infection * Prior organ allograft * Significant serious intercurrent illness unrelated to cancer or its treatment not covered by other exclusion criteria expected to significantly increase the risk of HSCT * Any mental or physical condition, in the opinion of the PI (or PI designee), which could interfere with the ability of the subject (or the only parent or legal guardian available to care for the subject) to understand or adhere to the requirements of the study * Enrollment in any other clinical study from screening up to Day 100 (unless PI judges such enrollment would not interfere with endpoints of this study) Exclusion Criteria for Donors: * Lactating females * Pregnant females