Liposomal Cytarabine, Daunorubicin, and Gemtuzumab Ozogamicin for the Treatment of Relapsed Refractory Pediatric Patients With Acute Myeloid Leukemia

Inclusion Criteria: * Pediatric patients with diagnosis of CD33 positive (\> 3%), * Newly diagnosed secondary AML * Relapsed refractory acute myeloid leukemia by World Health Organization (WHO) criteria Patients must have \>= 5% blasts in the bone marrow as assessed by morphology or flow cytometry. However, if an adequate bone marrow sample cannot be obtained, patients may be enrolled if there is unequivocal evidence of leukemia with \>= 5% blasts in the peripheral blood * Pediatric Patients with myelodysplastic syndrome (MDS) who progress to AML are eligible at the time of diagnosis of AML regardless of any prior therapy for MDS * Performance status: Lansky \>= 50 for patients who are =\< 16 years old and Karnofsky \>= 50% for patients who are \> 16 years old * Age =\< 21 years of age * Total serum bilirubin =\< 2 x upper limit of normal (ULN). Patients with known Gilbert's syndrome may have a total bilirubin up to =\< 3 x ULN * Serum creatinine =\< 2.0 mg/dl * Alanine aminotransferase (ALT) and/or aspartate aminotransferase (AST) =\< 3 x ULN; =\< 5 x ULN in case of suspected leukemic liver involvement * Females of childbearing potential must have a negative serum or urine beta human chorionic gonadotropin (beta-HCG) pregnancy test result within 14 days prior to the first dose of study drugs and must agree to use one of the following effective contraception methods during the study and for 30 days following the last dose of study drug. Effective methods of birth control include: * Birth control pills, skin patches, shots, implants (placed under the skin by a health care provider) * Intrauterine devices (IUDs) * Condom or occlusive cap (diaphragm or cervical/vault caps) used with Spermicide * Abstinence * Males, need to inform the doctor right away if the partner becomes pregnant or suspects pregnancy. While in this study and for 30 days after the last treatment the patient should not donate sperm for the purposes of reproduction. He will need to use a condom while in this study and for 30 days after the last treatment Exclusion Criteria: * History of another primary invasive malignancy that has not been definitively treated and in remission. Patients with non-melanoma skin cancers or with carcinomas in situ are eligible regardless of the time from diagnosis (including concomitant diagnoses) * Presence of clinically significant uncontrolled central nervous system (CNS) pathology such as epilepsy, childhood seizure, paresis, aphasia, stroke, severe brain injuries, organic brain syndrome, or psychosis * Evidence of active cerebral/meningeal disease. Patients may have history of CNS leukemic involvement if definitively treated with prior therapy and no evidence of active disease at the time of consent with at least 2 consecutive spinal fluid negative assessments for residual leukemia and negative imaging (imaging required only if previously showing evidence of CNS leukemia not otherwise documented by spinal fluid assessment) * Patients with a cardiac ejection fraction (as measured by either multigated acquisition scan \[MUGA\] or echocardiogram) \< 50% are excluded * Patients with total cumulative doses of non-liposomal daunorubicin, or other anthracycline equivalent, greater than 450 mg/m\^2 * Patients with uncontrolled, active infections (viral, bacterial, or fungal). Infections controlled on concurrent anti-microbial agents are acceptable, and anti-microbial prophylaxis per institutional guidelines are acceptable * Known active hepatitis B or C infection, or known seropositivity for human immunodeficiency virus (HIV) * Liver cirrhosis or other serious active liver disease or with suspected active alcohol abuse * Active acute/chronic graft-versus-host disease (GvHD) requiring systemic treatment; or receiving immunosuppression for GvHD prophylaxis within 2 weeks from the start of study therapy * Prior chemotherapy/radiotherapy/investigational therapy within 2 weeks before the start of study drugs with the following exception: * To reduce the circulating blast count or palliation: Single dose intravenous cytarabine or hydroxyurea. No washout necessary for these agents * Females who are pregnant or lactating * Male or female subjects of childbearing potential, unwilling to use an approved, effective means of contraception in accordance with institution's standards * Other severe, uncontrolled acute or chronic medical or psychiatric condition or laboratory abnormality that in the opinion of the Investigator may increase the risk associated with study participation or investigational product administration or may interfere with the interpretation of study results and/or would make the patient inappropriate for enrollment into this study * Patients with Down syndrome, acute promyelocytic leukemia, juvenile myelomonocytic leukemia, or bone marrow failure syndromes are not eligible