(Selling a car) What would you do in this situation?

I have a 99 ford ranger extended cab 4 door that is up for sale for $3500. I had it checked last month for any discrepancies and they rotated tires, etc. The only current issue is a 6th cylinder misfire. The car is spotless… No rust even. I had multiple people interested in the car, but were wary of the shaking due to the misfire so they passed. This older lady contacted me yesterday asking if I would let her mechanic check it out before committing. That sounded like a sound idea so I brought it, the mechanic drove it, and came back and said it" 'misses' otherwise in top shape. I will need to see what the issue" the woman asked "how much will that cost?" mechanic said "I… Depends on how long it takes to find the issue and what it is, could be the valve worst case, but that is highly unlikely.a signal issue, or a fuel injector issue" woman says "well how much to check any of those" mechanic says "I can't tell you, it depends, could be $200 or more, or less" lady says "okay, $200. Not $250 or $275" (she looks at me) "want to go down to $3000 and we can split the diagnosis cost?" I said "sounds fair" so we shook on it.

I dropped off the car this morning to get it looked and a few hours later, I got a random msg from the lady asking why I wasn't at the mechanics (?) I said "I dropped off the car this morning, I'm at work till 8 and haven't gotten a call yet" she says "they finished fixing it"… Why did she get a call before me? And why did they just go ahead and FIX it?

Added (1). Apparently she called a ton till they budged. She told me "well, I figured since I want the car, and the car was already there, may as well fix it" so SHE gave THEM the go ahead since she was going to be buying it anyway.
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I called the mechanic and he was already sick of it and I hadn't even called him before! He told me it was not DONE yet, but found it needed a 6th cylinder fuel injector piece and that was the problem, He said it would be ready tomorrow morning and he would call.

Added (2). He said it would be around $360.

I msged the lady and said it'd be $360 so she told me that since it was more than the $200 the mechanic 'promised', that I should down the price to compensate. She tried $2500 and said she would pay the $360 fee. I said "uh, no" and she was like "please. I can't do $3000… But but what about $2800? Right in the middle" and started getting all upset about a loan she is desperately having trouble getting cause someone stole her purse last month and blah blah.

Added (3). Now that it was fixed and in tip-top I feel like I'm in a quandary cause she is using the price of the fix as a bargaining chip against the price I had the vehicle at with a issue, now that it is all fixed I can easily get 5k for it. Only problem is I DON'T HAVE $360, nor did I agree to this stupid fix at this ma-and-pa shop. I agreed to it being diagnosed, for her piece of mind.

Added (4). From what I understand it is illegal for them to perform maintenance on it without written consent above $50 in the state of Iowa, not to mention the fact they took the consent from the woman who doesn't even own it.

So, you put nothing at all in writing with the mechanic regarding the diagnosis and repair? Your fault. If there was no express statement from you not to repair whatever fault was found, it makes sense that the mechanic would just go ahead and fix it if it wasn't anything major, and that's probably how he understood the situation. It seems to me that he actually saved you some time although I agree that he should have called you first. That's just common courtesy.

It sounds to me like you agreed to $3000 minus half the diagnosis cost. Everything else (i.e the other half of the diagnosis and the repair) is on her if she buys your rig. Otherwise, you pay everything, keep the truck, and look for another buyer. If you didn't put a sales agreement in writing, she can't hold you to it. The question is whether you need the extra few hundred badly enough to piss someone off by backing out of the handshake agreement this late in the game.

Sell it. Get rid of the truck. You will sleep better.