My girlfriend is "required" to work at least one holiday per year. For that day (new years) she is paid double time, HOWEVER her employer is forcing her to take an additional day off that week to avoid paying her the overtime.

Is this legal?

Yes it is. No law prevents an employer from rearranging the schedule to avoid incurring OT costs.

thank you so much for your response! Still pretty unethical, but unfortunately legal.

I don't agree that it's "unethical". Is it unethical for a business to try to control its labor costs by scheduling employees so that overtime pay is not due? Not in my opinion.

They have no legal obligation to pay any kind of premium for working on the holiday.

They have no legal obligation to pay any kind of premium for working on the holiday.

Let alone require the employee to work another day so that s/he gets OT.