I presume that your wife's attorney knows full well what the law is, and he/she has no doubt explained the chances of success to her.
In a case like this the mentality that you are facing is that this is an all or nothing proposition. Meaning that from your wife's perspective, she either will be entitled to roughly half of the inheritance, or she will be entitled to none of it. Since your stated position is that you are not willing to give her any of that, I'm sure that her thought and that of her attorney is that they might as well roll the dice because they have nothing to lose. It is this mentality that is creating the sticking point.
Of course, you run a risk of losing some of your inheritance, based on the whim of the mediator, or ultimately a judge.
If you want to streamline the divorce
process and hopefully avoid unnecessary legal fees, I suggest that you make it so that your wife does have something to lose by rolling the dice. Only you know what it might take to get her attention.
In theory at least, if you were to offer her 25% of the inheritance to walk away from the dispute that should be sufficient for her to capitulate and agree to your offer. 50% of something is usually better than a roll of the dice for all or nothing.
In your favor is the fact that you can document and trace the funds going in to the marital; account. Also, the courts are used to ruling that inheritances are intended by the testator to be separate property, and this is something that weighs in your favor.
It all boils down to whether you feel like gambling
on an unknown, versus taking a partial loss as insurance against the possibility of a bigger loss.
I wish you the best in resolving this issue to your benefit.