Brentuximab Vedotin and Gemcitabine Hydrochloride in Treating Younger Patients With Relapsed or Refractory Hodgkin Lymphoma

Inclusion Criteria: * Patients must have had histologic verification of the malignancy at original diagnosis; patients must have histologic verification of recurrent Hodgkin disease at the time of relapse; no additional biopsy is required for patients with primary refractory disease (i.e. no prior CR) * PARTS A AND B: Patients with Hodgkin lymphoma (HL) are eligible for both the phase 1 and 2 portions, if they are in one of the following categories: * Primary refractory disease (i.e. no prior CR) * Very early relapse (\< 6 months from the end of initial therapy, including chemotherapy ± radiation) * Advanced stage (III or IV) at diagnosis who relapse less than one year from the end of initial therapy * Note that patients with low-stage disease (IA or IIA) at initial diagnosis, who were treated with radiation alone or fewer than four cycles of chemotherapy will NOT be eligible * Patients must have measurable disease, documented by clinical and radiographic criteria * Patients must have a life expectancy of \>= 8 weeks (\>= 56 days) * 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 fully recovered from the acute toxic effects of all prior anti-cancer chemotherapy * At least 14 days after the last dose of myelosuppressive chemotherapy (28 days if prior nitrosourea); Note: cytoreduction with hydroxyurea can be initiated and continued for up to 24 hours prior to the start of therapy * 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 * At least 7 days after the last dose of a biologic agent; 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 * At least 42 days after the completion of any type of immunotherapy, e.g. tumor vaccines * At least 3 half-lives of the antibody after the last dose of a monoclonal antibody * At least 14 days after local palliative radiation therapy (XRT) (small port); at least 150 days must have elapsed if prior total body irradiation (TBI), craniospinal XRT or if \>= 50% radiation of pelvis; at least 42 days must have elapsed if other substantial bone marrow (BM) radiation * Patients with prior autologous or allogeneic stem cell transplant (SCT) are excluded from this study * At least 28 days must have elapsed since the most recent dose of bleomycin, to allow adequate time to detect evidence of bleomycin-related pulmonary toxicity * PART A: FOR PATIENTS WITH KNOWN BONE MARROW INVOLVEMENT (Completed as of Amendment 4) * Peripheral absolute neutrophil count (ANC) \>= 1000/uL * Platelet count \>= 100,000/uL (transfusion independent, defined as not receiving platelet transfusions for at least 7 days prior to enrollment) * PART B: FOR PATIENTS WITHOUT KNOWN BONE MARROW INVOLVEMENT * Peripheral absolute neutrophil count (ANC) \>= 750/uL * Platelet count \>= 75,000/uL (transfusion independent, defined as not receiving platelet transfusions for at least 7 days prior to enrollment) * Patients with lymphoma metastatic to bone marrow who have granulocytopenia, anemia, and/or thrombocytopenia will be eligible for study but not evaluable for hematologic toxicity (in Part A, there will be a maximum of one per cohort); such patients must meet the blood counts as in Part A (may receive transfusions provided they are not known to be refractory to red cell or platelet transfusions); if dose-limiting hematologic toxicity is observed, all subsequent patients enrolled in Part A must be evaluable for hematologic toxicity * 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: * =\< 0.6 mg/dL (for 1 to \< 2 years of age) * =\< 0.8 mg/dL (for 2 to \< 6 years of age) * =\< 1.0 mg/dL (for 6 to \< 10 years of age) * =\< 1.2 mg/dL (for 10 to \< 13 years of age) * =\< 1.4 mg/dL (for females \>= 13 years of age) * =\< 1.5 mg/dL (for males 13 to \< 16 years of age) * =\< 1.7 mg/dL (for males \>= 16 years of age) * Bilirubin (sum of conjugated + unconjugated) =\< 1.5 x upper limit of normal (ULN) for age * Serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) \< 2.5 x upper limit of normal (ULN) for age; for the purpose of this study, the ULN for SGPT is 45 U/L * Serum albumin \>= 2 g/dL * No evidence of dyspnea at rest, no exercise intolerance due to pulmonary insufficiency, and a pulse oximetry \> 92% while breathing room air * Forced expiratory volume in one second (FEV1)/forced vital capacity (FVC) \> 60% by pulmonary function test (PFT), unless due to large mediastinal mass from HL; carbon monoxide diffusion capacity (DLCO), FEV1, and forced vital capacity all \> 50% predicted value; Note: pulmonary function testing is not required for children \< 8 years old, or for any child who is developmentally unable to comply with pulmonary function testing * Patients with seizure disorder may be enrolled if on anticonvulsants and well controlled * Nervous system disorders (Common Terminology Criteria for Adverse Events \[CTCAE\] version \[v\] 4) resulting from prior therapy must be \< grade 2 Exclusion Criteria: * Pregnant or breast-feeding women will 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 contraceptive method during protocol therapy and for at least 30 days after the last dose of brentuximab vedotin; abstinence is an acceptable method of birth control * Concomitant medications * Patients receiving stable or decreasing corticosteroids are not eligible for other concurrent conditions (e.g. asthma, autoimmune diseases, rash, documented adrenal insufficiency) are eligible for this study * Patients who are currently receiving another investigational drug are not eligible * Patients who are currently receiving other anti-cancer agents are not eligible * Patients who have an uncontrolled infection are not eligible * Patients with an immunodeficiency that existed prior to diagnosis, such as primary immunodeficiency syndromes, organ transplant recipients and children on current systemic immunosuppressive agents are not eligible * Patients known to be positive for human immunodeficiency virus (HIV) are not eligible * Prior therapy * Patients with prior exposure to brentuximab vedotin are not eligible; NOTE: prior exposure to gemcitabine is NOT an exclusion criterion * Patients who have undergone prior autologous or allogeneic SCT are not eligible * Patients with HL who were stage IA or IIA at initial diagnosis and treated with either radiation alone or \< 4 cycles of chemotherapy are not eligible * Patients who have received a prior solid organ transplantation are not eligible * Patients with known hypersensitivity to Escherichia coli (E.coli)-derived proteins, filgrastim, or any component of filgrastim 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 * 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