Temozolomide or Selumetinib in Treating Patients With Metastatic Melanoma of the Eye

Inclusion Criteria: * Patients must have metastatic histologically or cytologically confirmed uveal melanoma; if histologic or cytologic confirmation of the primary is not available, confirmation of the primary diagnosis of uveal melanoma by the treating investigator can be clinically obtained, as per standard practice for uveal melanoma; pathologic confirmation of diagnosis will be performed at Memorial Sloan-Kettering Cancer Center (MSKCC) or at a participating site * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as \>= 20 mm with conventional techniques or as \>= 10 mm with spiral computed tomography (CT) scan * Life expectancy of greater than 3 months * Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 * Leukocytes \>= 3,000/mcL * Absolute neutrophil count (ANC) \>= 1,500/mcL * Platelets \>= 100,000/mcL * Hemoglobin \>= 9.0 g/dL (not requiring transfusions within the past 2 weeks) * Total bilirubin =\< 1.5 times upper limit of normal; note: patients with hyperbilirubinemia clinically consistent with an inherited disorder of bilirubin metabolism (e.g., Gilbert syndrome) will be eligible at the discretion of the treating physician and/or the principal investigator * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 times …