I went for appeal a couple of years back and reckon the system hasnt changed too much.
Your wife should get as much information together as possible for the appeal. She will have the right to get access to the medical assessment file that the doctor in the department completed during the exam that she underwent. This will tell her information that was recorded by the doctor during on the medical assessment. It also should tell the reason why the doctor considered her fit for work. Other records that exist may be a report from the medical certifier. The Department are suppose to notify the medical certifier of the exam and look for a medical report. All these records can be got through the freedom of information acts. Who was the doctor that certified your wife as unfit for work. A consultant would be more credible than a GP.
Very few cases that come to appeal are successful... I think the figure is around 10%. You will really have to know what you are doing - and pick flaws that may emerge in the departments decision. However, just because a medical certifier writes a certificate of incapacity that doesnt necessarily mean that a person is unfit for work - it depends on the nature of the work and whether the illness affects that persons ability to do their work - alot of GPs write certs as matter of course.
If your wifes case comes for oral hearing, the appeals officers are not doctors - crazy I know. More than likely your wife be sent back to for another medical examination in the department but this will be done by another doctor. Like you ask your GP questions - dont be afraid to ask these doctors questions and take note of everything they say and do. While your wife is entitled to an independent appeals process - this system as it currently stands does not allow for independent medical examinations for illness benefits appeal.
Your wife has two choices - put in the appeal if she is sick and cannot work - or accept the decision of the doctors in the Department and go back to work. Another thing to consider is whether the employer will accept her returning to work if its against medical advice.