Jerry, the terms you are looking for is a Prescriptive Right of Way, here in Florida, at least when you define the circumstances you and others have mentioned in this thread about using and maintaining someone elses (absent) land. It akin to Squatting, which is how a lot of underdeveloped countries still operate.
This is not an undeveloped country.
I stand by my original advice- You should know more than she does by educating yourself. You can get a fair bit of info right from your own civil servants, and probably not even speak with them in person or visit them at city hall. I have to hunt for a website that will let you search the municipal code, if I find it I will pass it on to you. It has had info in ever place I have ever looked, but I can't guarantee your state or town is a part of it. I believe it may. Even if you find the local code, it can be hard to read and interpret, for sure. I don't trust the Clerk at City Hall to know, and she won't be making a decision on a ruling, anyway. You need to know what the law is, and be prepared to have someone argue it for YOU. This is not a DIY thing.
Now to piss off a bunch of well meaning posters here.
All of you with advice who are actually lawyers, stand up. Of all of you standing, if you don't specialize in Real Law (that's Real Estate, and Family) sit back down. For the rest still standing, if you aren't licensed by the Minnesota State Bar Association, sit down.
With all these guys that are left standing up, you have lots of solid advice, don't you?
Practicing law without a license is actionable.
Sure with some of the stupid redneck manly-man empty threats you've gotten, there has been some sage advice that is realistic.
I work for the government, and I have to take peoples land with eminent domain constantly. In another career, I've been dragged into pissing matches over neighbors fighting over property lines as a business owner providing service, and even further with a different (simultaneous career) with a different govt agency, I've been in the middle of fights between the ADA, the US Fish and Game Comm, the DEP, the FFWCC and the Endangered Species Act. Years have past and there still isn't a solution, You know who's winning? The Lawyers.
If a consultation with a Real Law Attorney in the next town over (NEXT TOWN OVER) costs you 50-100 bucks, its worth it.
(That AC condenser and fence would have to go, period, thats YOUR land. The quarry land? The Quarry owner aint vacating it. The City alley may be vacated if the City wants to, but I find generally if has to be their idea, and since there doesn't seem to be a compelling reason, I doubt they will. Its not quick or cheap when they have so much work to do internally to get it done. Not to mention, any objections from anyone will make them back up from proceding, not worth anything to them. If I was a town official, I wouldn't entertain the request to vacate the alley)