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But it is acting as if it wasn't a mutual agreement.

Maybe "resignation" doesn't meet your criteria. But "firing" implied that the employee wanted to keep their job but the company ended it.

Would you accept "mutual termination" ?

It wasn't a mutual agreement. She wanted to keep her job until she was back from vacation at least.[1]

So she was fired after making demands the employer wasn’t prepared to meet, including keeping her employed until after her vacation.