My understanding of your question is that her employer withheld taxes for the City of Detroit. You indicated that she did not work or live in the City of Detroit and that there was an error with her address which caused her employer to withhold taxes for the City of Detroit. The simplest way to get the refund would be to file the City of Detroit indicating that you are not a resident of Detroit.
When answering the questions under the Detroit return you would answer them that she is a non-resident and did not work in the City of Detroit. When it asks how much of her income is for the City of Detroit enter a "0". The result would be that the return would issue a full refund of the taxes withheld.
You do not need a W2c, you can fie with the original W2 and just claim as none of it was for the City of Detroit.
