We have an employee that resigned two weeks ago and we accepted her resignation.  However, on her last day, she now wants to withdraw her resignation.  Can she do that?  Do we have to keep her?  We don't want to. 

Unless there is a union contract or policy that says otherwise, I think once they've resigned and you've accepted you can refuse to let them rescind the resignation. If they are at will you don't have to keep them regardless. I do wonder what will happen if she files for unemployment ....

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Barbie

Barbie is correct: if there is no contract (CBA or otherwise), or a policy  or practice in place to the contrary, that is: the person is in an un-constrained employment-at-will context, then you do not need to allow them to stay on board.

On the unemployment side, you will probably be fine when you say that you couldn't keep this person on because you had already hired a successor, who you couldn't simply fire when the incumbant changed their mind.

Alternatively, if the person who is trying to rescind their resignation has been a good employee and they have left professionally, then perhaps you should consider simply not responding to their UI claim.  In any event, based on what little I know, I wouldn't let them stay because whatever drew them away will still be out there in one form or another: they're a short timer.