It's a tricky one.
I understand your position, and I can see why you feel it is the responsibility of your friend, as the driver, to pay for the fine which you have not created in any way.
But if your friend is making a stand, and that is going to inconvenience you, which I guess it will, I'd be inclined to call her, say you've had second thoughts, and you don't want to fall out, so you will pay the half of the additional penalty.
It's always worth appealing any fine, especially if she can provide evidence that it was addressed incorrectly - so tell her to do that, and if she gets it quashed, she can give you half the money back.
I would try not to lose a friend, or a lift, and especially not both, even though you are morally right in your position in my view.
It's a matter of picking your battles, this one has 'lose' all over it for you, so time to make some amends.
Hope it works out for you.