Without reading every word above, naturally, one would want to first explain the issue to the head of the business that sold the car if they would please take care of this problem. That can work. You just never know unless you try. If they say there's nothing they can do, ask them who else you can talk to "up the food chain." People relate to that phrase, because everybody reports to somebody, until you get to the owner, but they will have to report to the manufacturer if this is a dealer. It's not a matter of being mean or threatening, but of letting them know that you will not leave anyone out in your search for help here. You're going to let everyone know what happened and ask everyone possible who is in some position of authority to help.
That said, I generally avoid dealers for everything, including used cars, but there are exceptions. If it's a car that they've been maintaining and they will show you the service records, etc. and they are asking a fair price, well, then, maybe.
Why avoid dealers? Well, one big reason is all those people in there sitting at computer monitors, sitting at desks, doing very little. How do all those salaries get paid? Well, by charging a lot, that's how! A competent garage is the way to go, in my experience.
What's a fair price for a used car? Some folks don't believe it, but there is an industry standard for that, and it avoids having to haggle and having to feel ripped off on both sides of the transaction. It's used by bank loan officers who grant car loans on used cars. It's used by dealers when they set used car prices. And it's used by buyers and sellers who know the scoop and don't want to haggle. That's the NADA price, available at nadaguides.com. It sounds too easy, but that's the fact.
The other important place to check is Consumer Reports because they use records of repairs of used cars when putting out their periodic used car reports. Look for cars with decent repair records, of course. Once a car is identified (say, on Craigslist, or wherever), I make an appointment for a look, but early on in the discussions, I tell them that if I decide I want the car and we agree on a price (but I just bring a printout from NADAguides.com for that car, with that mileage; and I might should have run the Carfax report on the car, for a small fee, but a carfax report only tells you about insurance claims; other damage not repaired under insurance, no. Carfax also can have maintenance records), then I will want to do a buyer's check by my mechanic, at my expense, and ask if that would be OK. (I get an idea of what a good, independent garage will charge for that, and an idea of how long it takes to get a car in for a buyer's check.) I explain that I would not do a buyer's check unless I really am serious about the car, and that I plan to buy it unless the buyer's check turns up something, in which case I'd be willing to talk about amending the price appropriately. Reasonable people just are fine with a mechanic's check; they'd do the same if roles were reversed. I often ask during the first phone call if a mechanic's check would be OK, presuming that I like the car and we agree on a price.