How do you not laugh in her face?! Honestly some parents are ridiculous!!

"As per our signed agreement, payment for vacation is due in full on XY date in order to not accrue late payment fees. As per the contract late fees are applied as follows.....blah blah. Enjoy your vacation and see you on XY date"

Stand your ground you will be better off for it. She is a bully. She knows what she signed up for, she is just trying to take advantage of you. 99.9% of providers charge per enrollment so she is not going to get lucky by going elsewhere.

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