Q: Is it possible for me to sue the woman that is accusing my husband of rape for Emotional Distress/Mental Anguish?
A: Anyone may sue anybody for anything at any time anywhere. Would you win? I doubt it since the bad person has done nothing to you. Plus the fact that "emotional distress/mental anguish" is generally not an independent tort. There must be an underlying tort.
These are exceptionally general answers.
You need to consult with a tort attorney in your area for full details.
There are two rules for success:
(1) Never tell everything you know.