Sounds as though if the leaking coil is replaced and it works, then it works. But of course we do not know more than what you wrote. Did they agree to replace the unit or fix it? A lot of times inspectors "recomend" replacement because it benefits them in long run so they can say, well I did reccomend that you replace the item. -or- a company that just wants to make the moeny off replacing the unit with no intention of fixing. Tough to say... Maybe a coil is all it needs.
But you need to have your attorney address the issue.
This is why it is important to use an attorney who specializes in real estate. Your attorney should be handling this issue and providing you with advice.
It doesn't sound like you got a home inspection because this is something that would have been discovered during a routine home inspection. If the air conditioning unit broke after the home inspection then I understand why it became an issue so late in the process. This is also a good example of why a home warranty is money well-spent.
If the replacement parts/unit is of reasonable quality and the work is done by a reputable company I am not sure why you would be so concerned about cost to the seller. You can always have the work done by a contractor of your choice at your cost.
I suggest you contact your attorney and follow his/her advice.