Mocetinostat With Vinorelbine in Children, Adolescents & Young Adults With Refractory and/or Recurrent Rhabdomyosarcoma

Inclusion Criteria:

* Willing and able to provide written Institutional Review Board (IRB)/Independent Ethics Committee (IEC)-approved informed consent. For subjects \< 18 years of age, their parents or legal guardians must sign a written informed consent. Assent, when appropriate, will be obtained according to institutional guidelines
* Have histologically or cytological confirmed diagnosis of rhabdomyosarcoma with locally advanced/unresectable, metastatic, refractory or relapsed disease who have failed standard therapy and for whom no known curative therapy exists
* Measurable disease according to RECIST version 1.1
* Prior cancer therapy: Subjects may have received any number of prior therapy regimens. In the investigator's opinion, subjects must have tolerated prior cytotoxic therapies well and have adequate bone marrow reserve. At the time of treatment initiation, at least 3 weeks must have elapsed after prior cytotoxic chemotherapy. At least 7 days must have elapsed since completion of any prior non-cytotoxic cancer therapy and any associated AEs must have resolved
* Prior radiotherapy is allowed if \>= 2 weeks have elapsed for local palliative radiation therapy (XRT) (small port); \>= 6 months must have elapsed if prior total body irradiation, craniospinal XRT or if \> 50% radiation of the pelvis; \> 6 weeks must have elapsed if other substantial bone marrow radiation (defined per principal investigator's \[PI's\] discretion). Subjects who have received brain irradiation must have completed whole brain radiotherapy and/or gamma knife at least 4 weeks prior to enrollment
* Subjects with controlled asymptomatic central nervous system (CNS) involvement are allowed in absence of therapy with anticonvulsants. Subjects not requiring steroids or requiring steroids at a stable dose (=\< 4 mg/day dexamethasone or equivalent) for at least 2 weeks are eligible
* Resolution of all acute toxic effects (excluding alopecia) of any prior anti-cancer therapy to National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) (version 4.03) grade \< 1 or to the baseline laboratory values as defined below
* Eastern Cooperative Oncology Group (ECOG) performance status (PS) =\< 2 in subjects \>= 17 years old; or Karnofsky/Lansky \> 50 in subjects \< 16 years old
* Subjects age \> 18 years for first cohort. Subjects must be \> 12 years old for the second and subsequent cohorts
* Life expectancy of at least 3 months
* Absolute neutrophil count (ANC) \>= 1000/mm\^3 (\>= 1.0 x 10\^9/L)
* Platelets (PLT) \>= 100,000/mm\^3 (\>= 100 x 10\^9/L) (transfusion independent, defined as not receiving platelet transfusions within a 7 day period prior to screening)
* Hemoglobin \> 9.0 g/dL (transfusions are allowed)
* Serum creatinine =\< 1.5 x upper limit of normal (ULN) or creatinine clearance \> 60 mL/min
* Total serum bilirubin =\< 1.5 x ULN; =\< 5 x ULN if Gilbert's syndrome
* Liver transaminases (aspartate aminotransferase \[AST\]/alanine aminotransferase \[ALT\]) =\< 2.5 x ULN; =\< 5 x ULN if liver metastases are present
* Pregnancy test if female of child-bearing potential negative within 7 days of starting treatment
* Cardiac ejection fraction \> 50% or shortening fraction \> 28% by echocardiography (ECHO) or multigated acquisition scan (MUGA)
* Females of child-bearing potential must have a negative pregnancy test during screening and be neither breastfeeding nor intending to become pregnant during study participation. Females of childbearing potential must agree to avoid pregnancy during the study and commit to abstinence from heterosexual intercourse or agree to use two methods of birth control (one highly effective method and one additional effective method) at least 4 weeks before the start of protocol therapy, for the duration of study participation, and for 6 months after the last dose of mocetinostat
* Males with partner(s) of childbearing potential must take appropriate precautions to avoid fathering a child from the screening period until 90 days after receiving the last dose of mocetinostat. They must commit to abstinence from heterosexual intercourse or agree to use appropriate barrier contraception
* Prior to enrollment of females or males of reproductive potential, the investigator must document confirmation of the subject's understanding of the possible teratogenic effects of mocetinostat
* Willingness and ability to comply with scheduled visits, treatment plan, laboratory tests and other study procedures

Exclusion Criteria:

* Current participation in another therapeutic clinical trial
* Symptomatic brain metastases
* History of previous cancer (non RMS), except squamous cell or basal-cell carcinoma of the skin or any in situ carcinoma that has been completely resected, which required therapy within the previous 3 years. Other low grade cancers can be reviewed and allowed at the discretion of the PI
* Incomplete recovery from any surgery (other than central venous catheter or port placement) prior to treatment
* Any of the following in the past 6 months: pericarditis, pericardial effusion, symptomatic congestive heart failure, cerebrovascular accident or transient ischemic attack, pulmonary embolism, deep vein thrombosis, symptomatic bradycardia, requirement for anti-arrhythmic medication
* History of prolonged corrected QT (QTc) interval (e.g., repeated demonstration of a QTc interval \> 450 milliseconds, unless associated with the use of medications known to prolong the QTc interval). QTc will be calculated using the Bazett formula (RR interval = 60/heart rate; QTI corrected = QT interval/sqr\[RRinterval\])
* History of additional risk factors for torsade de pointes (e.g., heart failure, family history of long QT syndrome)
* Use of concomitant medications that increase or possibly increase the risk to prolong the QTc interval and/or induce torsades de pointes ventricular arrhythmia
* Females who are breastfeeding/lactating
* Known active infections (e.g., bacterial, fungal, viral including hepatitis and human immunodeficiency virus \[HIV\] positivity)
* Other severe acute or chronic medical or psychiatric condition or laboratory abnormality that may increase the risk associated with study participation or study drug administration or may interfere with the interpretation of study results and, in the judgment of the investigator, would make the subject inappropriate for entry into this study or compromise protocol objectives in the opinion of the investigator and/or the sponsor