Haploidentical Hematopoietic Stem Cell Transplantation With Ex Vivo TCR Alpha/Beta and CD19 Depletion in Pediatric Hematologic Malignancies

Recipient Inclusion Criteria: * Must meet at least one of the following disease criteria: * B cell ALL in first remission and any of the following: * Persistent flow-based MRD at end-of-consolidation: * ≥ 1% for NCI SR ALL * ≥ 0.01% for NCI HR ALL * TCF3-HLF t(17;19) * KMT2A rearranged infant ALL, \< 6 months of age and presenting WBC of \> 300,000 or poor steroid response (peripheral blasts \>= 1000 /uL on day 8 of therapy * Other high-risk features not explicitly stated here, after discussion/approval with protocol PI. * B cell ALL in second remission and any of the following: * Early (\<36 months from start of therapy) marrow or combined relapse * Late (\>36 months from start of therapy) marrow or combined relapse with end-of re-induction flow MRD \>= 0.1% * Early isolated extramedullary relapse (\< 18 months from start of therapy) * Any B cell ALL in third or greater remission * T cell ALL in first remission * End-of consolidation MRD \> 0.1% * Any T cell ALL in second or greater remission * AML in first remission with any of the following high-risk features: * MRD ≥ 1% after first induction course * MRD ≥ 0.1% after second induction course * RPN1-MECOM * RUNX1-MECOM * NPM1-MLF1 * DEK-NUP214 * KAT6A-CREBBP (if \>= 90 days at diagnosis) * FUS-ERG * KMT2A-AFF1 * KMT2A-AFDN * KMT2A-ABI1 * KMT2A-MLLT1 * 11p15 rearrangement (NUP98 - any partner gene) * 12p13.2 rearrangement (ETV6 - any partner gene) * Deletion 12p to include 12p13.2 (loss of ETV6) * Monosomy 5/Del(5q) to include 5q31 (loss of EGR1) * Monosomy 7 * 10p12.3 rearrangement (MLLT10b - any partner gene) * FLT3/ITD with allelic ratio \> 0.1% * RAM phenotype as evidenced by flow cytometry: bright CD56+, dim to negative CD45 and CD38 and lack of HLA-DR * Other high-risk features not explicitly stated here, after discussion/approval with protocol PI. * AML in second or greater remission * Mixed phenotype or undifferentiated leukemia in any CR * Secondary to therapy-associated leukemia in any CR * NK cell lineage leukemia in any CR * Myelodysplastic syndrome (MDS) * Juvenile myelomonocytic leukemia (JMML) * May have undergone a prior hematopoietic stem cell transplant provided one of the criteria in Inclusion Criterion #1 are met AND the patient does not have active GVHD (has been off immunosuppression for at least 3 months). * Available familial haploidentical donor. * Donor and recipient must be identical at a minimum of one allele of each of the following genetic loci: HLA-A, HLA-B, HLA-Cw, HLA-DRB1, and HLA-DQB1. A minimum of 5/10 match is required and will be considered sufficient evidence that the donor and recipient share one HLA haplotype. * No more than 30 years of age * Lansky or Karnofsky performance status \> 50% * Adequate organ function as defined below: * Cardiac: LVEF ≥ 40% at rest or SF ≥ 26% * Hepatic: * Total bilirubin \< 3 x IULN for age * AST(SGOT)/ALT(SGPT) \< 5 x IULN * Renal: GFR ≥ 60 mL/min/1.73m2 as estimated by updated Schwartz formula for ages 1-17 years (see Appendix B), 24-hour creatinine clearance, or renal scintigraphy. If GFR is abnormal for age based on updated Schwartz formula, accurate measurement should be obtained by either 24-hour creatinine clearance or renal scintigraphy. Renal function may also be estimated by serum creatinine based on age/gender. A minimum serum creatinine of 2x upper limit of normal is required for inclusion on this protocol. * Pulmonary: * O2 saturation ≥ 92% on room air without positive pressure support * FEV1, FVC, and DLCO ≥ 50% of predicted (for children unable to perform a pulmonary function test, a high-resolution CT chest may be obtained) * The effects of these treatments on the developing human fetus are unknown. For this reason, patients of childbearing potential must agree to use adequate contraception (hormonal or barrier method of birth control, abstinence) prior to study entry and for 24 months following transplant. Should a woman become pregnant or suspect she is pregnant while participating in this study, she must inform her treating physician immediately. * Ability to understand and willingness to sign an IRB approved written informed consent document (or that of legally authorized representative, if applicable). Recipient Exclusion Criteria: * Available matched related donor. A patient with a matched unrelated donor is eligible if urgent transplantation is required. A prior unrelated donor search is not required for enrollment. * Active non-hematologic malignancy. History of other malignancy is acceptable as long as therapy has been complete and there is no evidence of disease. * Currently receiving any other investigational agents at the time of transplant. * Active CNS or extramedullary disease. History of CNS or extramedullary disease now in remission is acceptable. * A history of allergic reactions attributed to compounds of similar chemical or biologic composition to conditioning agents used in the study. * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection (bacterial, viral with clinical instability, or fungal), symptomatic congestive heart failure, or unstable cardiac arrhythmia. * Presence of significant anti-donor HLA antibodies per institutional standards. Anti-donor HLA Antibody Testing is defined as a positive crossmatch test of any titer (by complement dependent cytotoxicity or flow cytometric testing) or the mean fluorescence intensity (MFI) of any anti-donor HLA antibody by solid phase immunoassay. * Presence of a second major disorder deemed a contraindication for HSCT. * Pregnant and/or breastfeeding. Women of childbearing potential must have a negative pregnancy test within 14 days of the start of conditioning. Donor Eligibility Criteria: * At least 6 months of age * Meets the selection criteria as defined by the Foundation for the Accreditation of Hematopoietic Cell Therapy (FACT). * Able to understand and willing to sign an IRB-approved written informed consent document (or that of legally authorized representative, if applicable).