I would not. And to let you know, the other woman in my life has not been a picnic either. She has been stalking me for a year electronically, phone calls, letters, and finally walking in my house, on her own, to confront me about the affair in front of the kids.
Here is my take, you are dealing with an emotionally bankrupt person in the AP. Someone who was fine with the demeaning role of an adulterer just to steal your husband because pathetically in a world of people she thought your imperfect cheater was the answer to her dreams (think how pathetic, her dreams involve stealing a married man and wrecking a family to feel better about herself.) No matter what, this person is at least one nugget short of a happy meal.
Your silence by not taking the bait with these type of people makes you look stronger and in control. Engaging, gives her control, puts the ball back in her court. its a waste of time. she knows she is a loser and she doesn't care. No, sending her anything validates her behavior in a small way, don't validate her.
Ignore her. Focus on yourself and getting whatever outcome you decide you want in this marriage. No need to feel humiliated. You kept your composure, she did not.
By not engaging with this person, you look and are the better person, and both your husband and the other woman know this. You will dish out far more frustration by ignoring her. It sounds like all her interactions have been to get a reaction. Don't give her one.
The state of your marriage and the decisions to end it or repair it are the business of you, your husband and your children. She is just noise. Let it and her fade out of your life.