마음을 의지할 데가 없는 아이들은 ... = Those children who have no one to turn to for support ... = Those children who have no one to entrust their heart to ... * 의지하다 = 1) lean on or clutch something for physical support, 2) depend on someone/something for security, emotional comfort, etc. 마음을 의지하다 means to rely on someone emotionally for security, support, or comfort. 마음을 의지할 데가 없다 is saying you don't have anyone with whom you feel secure and comfortable.