You know, the more I think about this, the more annoyed it makes me. I do still think it's hilarious that she ever believed she could get away with saying her tiny little girl is that serious about the economy that she would refuse to attend a party, of course! But everything else about the situation is awful, and I really feel for her poor child.
Not only did this woman have the cheek to push for a change of venue for a child's birthday party, over a non-essential political preference and not something reasonable like a health need, she then asked again even after being told it's birthday boy's choice! The initial request alone is galling, but asking again is bloody bonkers. Let her serve sticks and leaves from some hippie pop-up at her own poor child's birthday.
But even that's not the worst of it in my opinion.
She is removing her child from a social event, simply to satisfy her own pretentious (imo) political preferences. She's not fooling anybody with that 'my 9yo is extremely politically involved - sorry, she's put her foot down and won't be moved' bollocks. She is stealing her little daughter's opportunity to go out and have a fun, special time with her mates, because she refuses to support one corporate chain, one bloody time. Her poor little girl, losing out on fun and friends because of her mum's shallow virtue signalling. It's shameful!
And even IF it were true - which, surely it is not - that the little girl is opposed (deeply or otherwise) to frequenting corporate chains, and so much so that she would choose to forego a friend's birthday party, then that in itself is a massive problem, in my opinion, too! Let your child be a child! She's only 9 ffs! With a mother who would make such a stand, there's no chance that she ever would have come up with such an opinion all on her own; surely mum will have fed it all to her. But why put that onto a child? Why on earth should that poor little girl bear all the weight of the world at such a young age? A little child should never be thinking about anything so heavy and dull as the effects of corporate versus local business patronage and the bloody economy! Let her have her innocence and fun while she's a child; she's got the rest of her life to worry about things she can barely affect anyway. It's just not right for a little child of only 9 to feel that strongly about things like economical issues!
Of course we should all do our part, and I do actually believe in, and even take part in, supporting local businesses, but everything in moderation, and I wouldn't put my DC out over it. For one thing, it would make no difference in the grand scheme if she set her political beliefs to one side on one occasion so that her little 9 year old daughter could go and have fun with her mates. For another, what makes the individual PE employees' jobs less worthy of her support than those employed at a locally owned private business? What would happen if everyone thought the way she did and avoided PE and other places like it? They'd go under, and hundreds if not thousands of local jobs would be lost! Corporate chain employees themselves are all working locally, all living and spending locally, all contributing to the local economy. So it doesn't really make sense to boycott them so absolutely anyway; it's superficial.
And I do hope, for her poor sweet and "shockingly economically and politically conscious" 
little girl's sake that she was communicating with you via a locally sourced, home grown, hand built device!
(Sorry, that was a bit of a rant. This woman really got up my arse though!)