How can I tell if my misbehaving child has an emotional disorder?

Try this. If your child has behavioral problems in other settings, such as day care, schools, friends homes etc, when you are not present this is a red flag. If only with you present, it still is a problem, but less likely to be an emotional disorder.
Your pediatrician. Should have Vanderbilt or other checklists for you & the teacher to complete to screen or assess for a neurodevelopmental disorder or mental illness. After reviewing health, growth, developmental, behavioral & family history, performing physical & neurological exams & discussing your discipline practices & family stresses, (s)he then refers to an appropriate mental health provider, if necessary.
Try a good book. I can recommend a good e-book. It's called: parenting the kids according to a child psychiatrist. It's available on kindle for only $5.95, I think you will find it to be a tremendous help and good luck. Also, check out on amazon the dvd called: the 20 minute behavioral miracle.