10-15 years ago…when I heard old, I was thinking a minimum of 50 years!
There is a lot more to understand here, more than you can easily describe here, so you need some local help.
You probably need a land use attorney, though you might find a local engineer well versed in land development who you could point you in the right direction, for a nominal fee (or might give you some free advice).
While seemingly a straight-forward situation, there is a lot to understand. Is this garage attached to the home? Or is it an accessory structure? A non-habitable accessory structure can have different setback requirements than the primary habitable structure. And which yard is it in - front, side, rear?
If the paperwork possibly existed, and is lost, it could be tough to prevail. And I have seen, even in the case of very new construction that violates zoning, rarely will someone be ordered to tear down a structure. A fence, perhaps yes, because removing or moving a fence is not a huge expense. Tearing down something that may have cost tens or hundreds of thousands, and has existed for a decade or more without any objections - typically doesn’t happen, even if technically it should happen.
I have seen plenty of neighbor issues such as this, and depending upon the circumstances, it may or may not be worth the fight. These things get very personal, and while I understand the feelings (DH is having such feelings right now about some neighbor improvements), it could be valuable to discuss with an attorney or engineer to get a neutral, outside view.
Please consider too if you prevail, you still have to live in the neighborhood (assuming you are not about to move across the country). And discuss the issues you are having due to the proximity of the garage with an engineer.
While it not is legally incumbent upon you to address the problems with measures on your side of the property line, I have seen situations where neighbors fight, and spend tens of thousands on lawyers and engineers, when they could have largely resolved the situation by spending a few thousand on their property. You’ll still be angry about the principle of the thing, though you won’t have funded vacations for some attorney.