Ok psycho Lulu
I did not, for one second, thought of you as a person that would just let her stay home and do NOTHING. I was generalising (sp - is that a word??) You sound like you handle her school and sick days like my parents did. Hence why we NEVER got sick on a Friday, because then you have to stay in bed the whole weekend.
I hear your frustration about the school not upholding their end of the "relationship" so to speak. That is not good. But like I say, don't ask, just tell the school she will not be attenting that last week, because she is needed else where. She is after all your child and they can't do anything about it, perhaps bore you to death with the "it's not ok to say away" thing.
See here comes in that silly white-lie thingy. You could tell them that she must start her vacation job (not really a lie - helping a aunt with a baby could be a babysitting job?!?)
Good luck