I'm going to schedule a vacation that overlaps with a coworker's and thus cut hers a bit short
Why would you want to plan a vacation during that time?
She deserves it.
Scheduling your vacation to overlap with your coworker's so she has to end hers early is really rude. You should try to plan around when your coworker's vacation is planned for, so that both of you can enjoy your time off to the fullest extent.
I want to spite my coworker, I don't care about her.
What you are doing is pet and wrong. You should talk to your co-worker and not try to ruin their vacation plans.