A study to learn about safety and find out maximum tolerable dose of palbociclib given in combination with chemotherapy (temozolomide with irinotecan or topotecan with cyclophosphamide) in children, adolescents and young adults with recurrent or refractory solid tumors (phase 1). Neuroblastoma tumor specific cohort to further evaluate antitumor activity of palbociclib in combination with topotecan and cyclophosphamide in children, adolescents, and young adults with recurrent or refractory neuroblastoma. Phase 2 to learn about the efficacy of palbociclib in combination with irinotecan and temozolomide when compared with irinotecan and temozolomide alone in the treatment of children, adolescents, and young adults with recurrent or refractory Ewing sarcoma (EWS).