Do not tell her. Absolutely, do not tell her!
I know that she trash talked me to another potential employer so I
don't feel comfortable telling her where I'm going to be working.
This is precisely the reason you should not tell her. What she did was not only immoral, but also completely illegal.
Not only you should not tell her, but you should be prepared for this person to harass your former colleagues and lie to your family and friends about needing to reach you in an emergency to get at this information. So if I were you, I wouldn't tell anyone else where you're going, so as not to put them in that situation.
You don't have to explain or justify yourself to her (or even to others in that company). And if she demands that you go to an exit interview, or sign a piece of paper, know that you don't have to do any of that. Don't feel pressured into doing anything during this notice period. And if the pressure feels bad at any point, forget the notice period and walk away.
Furthermore, if you feel this situation could still escalate, know that you could hire a lawyer to put them on notice to never badmouth you again. A good lawyer would even hire an impartial third party reference checking service to see how bad the badmouthing is.