Inclusion Criteria:

* Patients must be newly diagnosed with histologically-proven hepatoblastoma
* In emergency situations when a patient meets all other eligibility criteria and has had baseline required observations, but is too ill to undergo a biopsy safely, the patient may be enrolled on AHEP0731 without a biopsy

* Clinical situations in which such emergent treatment may be indicated include, but are not limited to, the following circumstances:

* Anatomic or mechanical compromise of critical organ function by tumor (e.g., respiratory distress/failure, abdominal compartment syndrome, urinary obstruction, etc)
* Uncorrectable coagulopathy
* For a patient to maintain eligibility for AHEP0731 when emergent treatment is given, the following must occur:

* The patient must have a clinical diagnosis of hepatoblastoma, including an elevated alpha fetoprotein, and must meet all AHEP0731 eligibility criteria at the time of emergent treatment
* Patient must be enrolled on AHEP0731 prior to initiating protocol therapy; a patient will be ineligible if any chemotherapy is administered prior to AHEP0731 enrollment
* If the patient receives AHEP0731 chemotherapy PRIOR to undergoing a diagnostic biopsy, pathologic review of material obtained in the future during either biopsy or surgical resection must either confirm the diagnosis of hepatoblastoma or not reveal another pathological diagnosis to be included in the analysis of the study aims
* Patients will be staged for risk classification and treatment at diagnosis using Children's Oncology Group (COG) staging guidelines
* At the time of study enrollment, the patient's treatment regimen must be identified; if the patient's primary tumor was resected prior to the day of enrollment and a blood specimen for the determination of serum alpha fetoprotein was not obtained prior to that surgery, the patient will be considered to have alpha fetoprotein of greater than 100 ng/mL for the purpose of treatment assignment; if tumor samples obtained prior to the date of enrollment were not sufficient to determine whether small cell undifferentiated (SCU) histology was present, treatment assignment will be made assuming SCU is not present in the tumor
* For patients with stage I or II disease, specimens for rapid central review have been submitted and the rapid central review diagnosis and staging must be available to be provided on the AHEP0731 eligibility case report form (CRF)
* Patients must have a performance status corresponding to Eastern Cooperative Oncology Group (ECOG) scores 0, 1, or 2; use Karnofsky for patients \> 16 years of age and Lansky for patients =\< 16 years of age
* Patients may have had surgical resection of some or all sites of hepatoblastoma prior to enrollment
* Organ function requirements are not required for enrolled patients who are stage I, PFH and will not be receiving chemotherapy
* Creatinine clearance or radioisotope glomerular filtration rate (GFR) \>= 70 mL/min/1.73 m\^2 OR serum creatinine based on age/gender as follows:

* 1 month to \< 6 months: 0.4 mg/dL
* 6 months to \< 1 year: 0.5 mg/dL
* 1 to \< 2 years: 0.6 mg/dL
* 2 to \< 6 years: 0.8 mg/dL
* 6 to \< 10 years: 1 mg/dL
* 10 to \< 13 years: 1.2 mg/dL
* 13 to \< 16 years: 1.5 mg/dL (male) or 1.4 mg/dL (female)
* \>= 16 years: 1.7 mg/dL (male) or 1.4 mg/dL (female)
* Total bilirubin \< 1.5 x upper limit of normal (ULN) for age
* Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) or serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) \< 10 x ULN for age
* Absolute neutrophil count (ANC) \> 750/uL
* Platelet count \> 75,000/uL
* Shortening fraction \>= 27% by echocardiogram
* Ejection fraction \>= 47% by radionuclide angiogram (multi gated acquisition scan \[MUGA\]); Note: the echocardiogram (or MUGA) may be done within 28 days prior to enrollment
* Serum triglyceride level =\< 300 mg/dL (=\< 3.42 mmol/L)
* Serum cholesterol level =\< 300 mg/dL (7.75 mmol/L)
* Random or fasting blood glucose within the upper normal limits for age; if the initial blood glucose is a random sample that is outside of the normal limits, then a follow-up fasting blood glucose can be obtained and must be within the upper normal limits for age
* Normal pulmonary function tests (including diffusing capacity of the lungs for carbon monoxide \[DLCO\]) if there is clinical indication for determination (e.g. dyspnea at rest, known requirement for supplemental oxygen); Note: for patients who do not have respiratory symptoms or requirement for supplemental oxygen, pulmonary function tests (PFTs) are NOT required
* Patients with seizure disorder may be enrolled if on non-enzyme inducing anticonvulsants and if seizures are well controlled
* Prothrombin time (PT) \< 1.2 x ULN
* All patients and/or their parents or legal guardians must sign a written informed consent
* All institutional, Food and Drug Administration (FDA), and National Cancer Institute (NCI) requirements for human studies must be met

Exclusion Criteria:

* Patients with stage I or II disease who do not have specimens submitted for rapid central pathology review by day 14 after initial surgical resection
* Patients that have been previously treated with chemotherapy for hepatoblastoma or other hepatoblastoma-directed therapy (e.g., radiation therapy, biologic agents, local therapy \[embolization, radiofrequency ablation, laser\]) are not eligible
* Patients who have received any prior chemotherapy are not eligible
* Patients who are currently receiving another investigational drug are not eligible
* Patients who are currently receiving other anticancer agents are not eligible
* Patients who have previously received a solid organ transplant are not eligible
* Patients who have an uncontrolled infection are not eligible
* Females who are pregnant or breast feeding are not eligible for this study
* Female patients of childbearing potential are not eligible unless a negative pregnancy test result has been obtained
* Males and females of reproductive potential are not eligible unless they have agreed to use an effective contraceptive method
* Patients receiving corticosteroids are not eligible; patients must have been off corticosteroids for 7 days prior to start of chemotherapy
* Patients who are currently receiving enzyme inducing anticonvulsants are not eligible
* Patients must not be receiving any of the following potent cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP3A4) inducers or inhibitors: erythromycin, clarithromycin, azithromycin, ketoconazole, itraconazole, voriconazole, posaconazole, grapefruit juice or St. John's wort
* Patients who are currently receiving therapeutic anticoagulants (including aspirin, low molecular weight heparin, warfarin and others) are not eligible
* Patients who are currently receiving angiotensin-converting enzymes (ACE) inhibitors are not eligible
* Patients must not have had major surgery within 6 weeks prior to enrollment on the high risk stratum; patients with history of recent minor surgical procedures (vascular catheter placement, bone marrow evaluation, laparoscopic surgery, liver tumor biopsy) will be eligible