Yep,
The buyer hasn't got a leg to stand on. I could sit all day here telling stories of my 8 years selling new & used cars of the stuff people tried to pull, I will limit it to a few precise statements.
This is what happens when you buy a used car, in particular when you were 100% crystal clear that there were engine leaks, we are now talking almost half a year later AND the fact that you already gave $800 bucks off the price of the car at the time of the transaction. There's the half of your $1500 my dear. This is a person to person used car sale. You are neither a dealer nor a mechanic, just one person selling a car to another one on a heavily implied "as-is, where is" basis.
Even if she bought it from a dealer, without some kind of explicit warranty purchased, there is little to no implied obligation. I had a few instances where stuff broke right away and we would fix it, but after a few weeks, nah. It's a used car!!! Smart dealers will explain cheap warranty options from companies like Lubrico, Ensurall or Trans-Canada starting from say a $79 3 month/5,000 km powertrain warranty and have all customers sign off a form declining it if they don't take it. That way their arse's are plenty covered. That kind of documentation is rock solid in front of a judge.
As a rule of thumb whenever I sell one of my vehicles, the bill of sale with whoever is buying it (in Ontario our UVIP documents provide for this) includes the words "Vehicle sold as-is, where is, no warranties of any kind mentioned or implied". If I am supplying safety and emissions certificates, then it will also read "3rd party Ontario Safety Standards and Drive-Clean certificates provided".
Otherwise, what is she looking for? Did she think for some reason that a $4200 used car with clearly stated issues was going to be infalable? I get that $4200 doesn't fall from the sky, but as Mike says were you expecting perfection? 4200 bucks is barely 30% of even the least expensive of new cars.
It sucks that you're in a small town; gossip, rumour and conjecture are likely spread like manure flowing downhill.