This is actually quite a sad saga, all caused by CF mum trying to manipulate Whiskey, who quite rightly refused to be her puppet.
Whiskey - FWIW I think you've handled this very well indeed. You did your best to enable the girls' friendship to continue, even though you realised that you and CF would never again have the same "friendly" relationship. CF chose to respond by upping her game and becoming more and more belligerent.
The moment she involved the girls, and the bullying started would have been he "gloves off" point for me - but you still managed to keep your cool, you still offered transport as long as they got to your home by 6 and made it clear that you would give a lift back, if they preferred to go by taxi.
CF didn't even have the courtesy to reply. She thought she had you on the back foot, I think, when you didn't go inside for a coffee. You were upset and she knew it, and thought that she could regain control by making you wait for her. I think her chat with the organiser was purely cosmetic - just to keep you in your place. She didn't for a moment think that you would drive off and leave them. But you did - good for you! Had she had you waiting outside for even 5 minutes, without her even having the good manners to apologise by text for holding you up, or asking via her DD if you would mind waiting for a few minutes, then she would have regained the upper hand (her previous actions the week before, when she and CFDD just got into your car without a word and sat almost in silence during the journey says that she was "punishing" you, and letting you know you couldn't get away with it.
You did the right thing not to wait when she hadn't asked you to. For all you know, she could have been half an hour. For all she knew, you needed to get home for a particular reason and couldn't hang about.
You have now shown that you will not be manipulated and bullied. She won't like that at all. I suspect that she is one of those people who would die (or kill) rather than apologise and "lose face", so if she can't get another chauffeur it's likely that CFDD will stop going to the group. Which is a shame, but that is her choice.
Be alert, though for
a) bullying of your DD at school - particularly attempts to isolate her
b) CF badmouthing you to all and sundry with her distorted version of what has happened
As I say - it is sad, more than anything. You and your DD regarded CF and CFDD as friends; you all got along and had a "working" relationship (so to speak), and pure because of the selfish determination of CF to have her own way, the whole lot is destroyed.
I agree that you should make it clear that you will not be looking after CFDog - and do it soon, so that she can't claim that you let her down at the last moment.
But can I say, I think that, despite what other posters feel, you stepped back from the drama on here very neatly indeed. You didn't allow yourself to be rushed into angry or hurt responses, as far as I could see, and considered what was best and kindest for the two girls as much as you could. But sometimes, you just have to take a stand and say "This is enough. It goes no further".
A sorry state of affairs, but not of your making.