many of us have garage shops.
You need to sort out the issues. Is the City's complaint based on the fact there is a shop in the garage or that your wife is using it for "business"?
Many of us have hobby shops and do very little business and almost none of it in the actual shop. Having "walk in trade" may be the distinction. Keeping a low profile for a while may be good advice. Hopefully the City will lose interest and move on.
Can't think of a city ordinance that actually requires you to put you car in the garage. They do have regulations about off street parking but you appear to have this covered.
I had a run in with an HOA on a rental I own. They raised the fee $8 and I failed to notice. After 90 days they took me to court for $24. I went to the court to pay it and the Clerk said "Nobody likes their HOA."
They are Tiny Tirants. You will not win. They will not be beaten. They may have long memories.
The neighborhood meeting maybe a god idea too if you can keep it friendly and calm.