As I admit, I agreed to that.
I'd be very surprised if the contract between you calls for you to pay when she has fundamentally breached it. Infact, the contract is likely no longer valid. You pay her to mind your child in loco parentis when you are not present. She misrepresented where he was, and what he did, and then tried to get him to lie to you.
I think for other people, her brazen brass neck is amusing - it's almost the shock value. For you, it's more personal and therefore not funny.
Re the zoo, you caught them just after their PR team left yesterday, so they wouldn't have wanted to respond without guidance. As it got hugely popular overnight, they'll have got PR to sign off a response to put there, rather than replying to the hundreds of emails that they've probably got asking if it's real. They probably won't know that you are the "real" person affected by this, and they''ll be reassured that there isn't mass fake ticket fraud going on.
How you handle this now is entirely up to you - you've probably got some reporting to do, when you feel up to it, and it might be legally advisable to give notice in writing and explain clearly why, but you don't need to do anything now if you'd rather spend the day with your son.
Have a good day.