Wee1 Kinase Inhibitor AZD1775 and Combination Chemotherapy in Treating Children, Adolescents and Young Adults With Relapsed or Refractory Acute Myeloid Leukemia

Inclusion Criteria: * Patients must have had histologic verification of AML at original diagnosis; AML is defined according to World Health Organization (WHO) classification with \>= 5% blasts in the bone marrow (M2/M3 bone marrow), with or without extramedullary disease * Relapsed patients: * Second or greater relapse OR * AML in first relapse AND has received \>= 450 mg/m\^2 daunorubicin equivalents * NOTE: for the purposes of determining eligibility for this protocol, the following cardiotoxicity multipliers will be used to determine daunorubicin equivalents: * Doxorubicin: 1 * Mitoxantrone: 3 * Idarubicin: 3 * Epirubicin: 0.5 * Refractory patients: * Patients must have received at least two attempts at remission induction, which may consist of up to two different therapy courses; Children's Oncology Group (COG) AAML1031 de novo therapy including induction I and induction II is one remission attempt * Patients must have the status of central nervous system (CNS)1 or CNS2 only, and no clinical signs or neurologic symptoms suggestive of CNS leukemia, such as cranial palsy * Patients must have a body surface area \>= 0.35 m\^2 at the time of study enrollment * Patient's current disease state must be one for which there is no known curative therapy or therapy proven to prolong survival with an acceptable quality of life * Karnofsky \>= 50% for patients \> 16 years of age and Lansky \>= 50 for patients =\< 16 years of age; patients who are unable to walk because of paralysis, but who are up in a wheelchair, will be considered ambulatory for the purpose of assessing the performance score * Patients must have recovered from the acute toxic effects of all prior chemotherapy, immunotherapy, stem cell transplant or radiotherapy prior to entering this study; all prior treatment-related toxicities must have resolved to =\< grade 2 or meet the inclusion/exclusion criteria prior to enrollment * Myelosuppressive chemotherapy: * Must be 14 days after the last dose of myelosuppressive chemotherapy (excluding hydroxyurea) * Cytoreduction with hydroxyurea can be initiated and continued for up to 24 hours prior to the start of therapy * Intrathecal cytotoxic therapy: * No waiting period is required for patients having received intrathecal cytarabine, methotrexate, and/or hydrocortisone * At least 14 days must have elapsed since receiving liposomal cytarabine (DepoCyte) by intrathecal injection * Intrathecal cytarabine given at the time of diagnostic lumbar puncture (LP) to evaluate for relapse prior to study enrollment is allowed * Biologic (anti-neoplastic agent): * At least 7 days since the completion of therapy with a biologic agent such retinoids, or DLI (donor lymphocyte infusion without conditioning) * Note: for agents that have known adverse events occurring beyond 7 days after administration, this period must be extended beyond the time during which acute adverse events are known to occur * Interleukins, Interferons and Cytokines (other than hematopoietic growth factors): * \>= 21 days after the completion of interleukins, interferon or cytokines (other than hematopoietic growth factors) * Antibodies: * \>= 21 days must have elapsed from infusion of last dose of antibody, and toxicity related to prior antibody therapy must be recovered to grade =\< 1 * Radiation therapy (RT): * At least 14 days after local palliative x-ray telescope (XRT) (small port); at least 84 days must have elapsed if prior traumatic brain injury (TBI), craniospinal XRT or if \>= 50% radiation of pelvis; at least 42 days must have elapsed if other substantial bone marrow (BM) radiation * Stem Cell Transplant (SCT) without TBI: * No evidence of active graft vs. host disease and at least 84 days must have elapsed after transplant or stem cell infusion * Patients must be off all systemic immunosuppressive therapy for at least 2 weeks, excluding hydrocortisone for physiologic cortisol replacement * Growth factors: * At least 14 days after the last dose of a long-acting growth factor (e.g. Neulasta) or 7 days for short-acting growth factor; for agents that have known adverse events occurring beyond 7 days after administration, this period must be extended beyond the time during which adverse events are known to occur; the duration of this interval must be discussed with the study chair * Patients must not have received prior exposure to AZD1775 * Platelet count \>= 20,000/mm\^3 (may receive platelet transfusions); these patients must not be known to be refractory to red cell or platelet transfusion * Creatinine clearance or radioisotope glomerular filtration rate (GFR) \>= 70 mL/min/1.73 m\^2 or a serum creatinine based on age/gender as follows: * Age: maximum serum creatinine (mg/dL) 1 to \< 2 years: 0.6 (male), 0.6 (female) 2 to \< 6 years: 0.8 (male), 0.8 (female) 6 to \< 10 years: 1 (male), 1 (female) 10 to \< 13 years: 1.2 (male), 1.2 (female) 13 to \< 16 years: 1.5 (male), 1.4 (female) \>= 16 years: 1.7 (male), 1.4 (female) * Bilirubin (sum of conjugated + unconjugated) =\< 1.5 x upper limit of normal (ULN) for age * Serum glutamic pyruvic transaminase (SGPT) (alanine aminotransaminase \[ALT\]) =\< 225 units per liter (U/L); for the purpose of this study, the ULN for SGPT is 45 U/L * Serum albumin \>= 2 g/dL * All patients and/or their parents or legally authorized representatives must sign a written informed consent; assent, when appropriate, will be obtained according to institutional guidelines * Specimens for cytogenetic analysis are required, and must be obtained prior to therapy initiation; for patient with refractory disease, the diagnostic specimen may be used Exclusion Criteria: * Pregnancy or breast-feeding: * Pregnant or breast-feeding women may not be entered on this study; pregnancy tests must be obtained in girls who are post-menarchal * Males or females of reproductive potential may not participate unless they have agreed to use an effective double barrier contraceptive method for the entire duration of protocol therapy * Corticosteroids should not be used as anti-emetic therapy; corticosteroid therapy is not permissible except for the following indications: * As treatment or prophylaxis for anaphylactic reactions * As a treatment for symptoms of cytarabine (Ara-C) syndrome (including fever, rash, or conjunctivitis) * Physiologic replacement stress-dosing as indicated for suspected or confirmed adrenal insufficiency * Patients who are currently receiving another investigational drug are not eligible * Patients who are currently receiving other anti-cancer agents are not eligible except for hydroxyurea (which may be continued until 24 hours prior to start of protocol therapy) * Anti-graft versus host disease (GVHD) agents post-transplant: * Patients who are receiving cyclosporine, tacrolimus or other agents to prevent graft-versus-host disease post bone marrow transplant are not eligible for this trial * Patients must be off all systemic immunosuppressive therapy for at least 2 weeks, excluding hydrocortisone for physiologic cortisol replacement * Patients who are currently receiving drugs that are strong or moderate inhibitors and/or inducers of cytochrome P450 family 3 subfamily A polypeptide 4 (CYP3A4) or sensitive CYP3A4 substrates and CYP3A4 substrates with a narrow therapeutic range are not eligible; the use of aprepitant as an antiemetic is prohibited due to early drug interaction data demonstrating increased exposure to AZD1775; caution should be exercised with concomitant administration of AZD1775 and agents that are sensitive substrates of cytochrome P450 family 2 subfamily C polypeptide 8 (CYP2C8), family 2 subfamily C polypeptide 9 (2C9) and family 2 subfamily C polypeptide 19 (2C19), or substrates of this enzyme with narrow therapeutic ranges, as well as agents that are inhibitors or substrates of P-glycoprotein (P-gp) * Patients must not have received enzyme inducing anticonvulsants for at least 14 days prior to enrollment * Patients must be able to swallow capsules whole; nasogastric or gastrostomy (G) tube administration is not allowed * Patients who have an uncontrolled infection are not eligible * Patients with any of the following diagnoses are not eligible: * Acute promyelocytic leukemia (APL) * Down syndrome * Fanconi anemia, Kostmann syndrome, Shwachman syndrome or any other known bone marrow failure syndrome * Wilson's disease and any other disorder of copper metabolism * Juvenile myelomonocytic leukemia (JMML) * Patients who have received a prior solid organ transplantation are not eligible * Patients who in the opinion of the investigator may not be able to comply with the safety monitoring requirements of the study are not eligible