If you have a good contract, you could certainly enforce it, but in this particular instance I'd probably proceed in the manner you have suggested for the very astutely-observed reasons you've stated - Cut your losses and offer a full refund, but by no means should you discount.He obviously does not see the value that she does, and if he wants to dictate everything about her day, then I'm not sure I want ot be a part of it. I will be sure to get a termination letter if it ends up that way.
By doing this, you convey your confidence in your your value AND get to show the client a little flexibility. This puts the ball firmly in their court - either they hire you at the agreed-upon rate or continue shopping. (In some circles, this is called the "take-away" close, and is very effective.)
The one thing that could have gone better on your end is to more thoroughly qualify the prospect and get buy-off from both decision-makers, or at least get her to commit herself as being able to make this decision unilaterally. If she told you that he'd be fine with it, she would have a much harder time coming back trying to re-work things.