What testing should my child undergo for suspected mitochondrial disease?  

Consult a specialist. Mitochondrial diseases are quite complicated and best evaluated at a specialized research center or a university medical center. The united mitochondrial disease foundation website (www.Umdf.Org) lists several types of blood and urine tests, heart echo (ultrasound), brain mri, eye and audiology exams, heart ekg, spinal fluid tests, chromosome tests, muscle biopsy, etc... As possible test choices.
Skin biopsy. There are a few research labs located around the country that will do the specialized testing needed for diagnosis. Often they need a sample of tissue to analyze the mitochondria within. This can be worked out through your local provider or specialty center.