I’m sorry to hear your wife’s application was incorrectly rejected. Have you contacted the embassy by phone or email? If you are unable to get a response from them, I recommend getting assistance in ding so, for example from a migrant counselling service, to advocate on your behalf in German with the embassy. It is important to emphasise that the visa rejection was incorrect and that it is not just the past 8 weeks you have been waiting, but rather the entre time since they rejected the application. This has led to an unnecessarily long family separation and should be corrected as soon as possible.
Here you can find an advisory service if you need assistance in contacting the embassy in German:
If an authority does not act on an application within 3 months without reasonable grounds, you can file a complaint called an ‘Untätigkeitsklage’. Here is some more information (via Wikipedia and an online translation, not an authoritative legal source):