On what basis can you fire her? Has she broken a company rule or policy? What normally happens when employees start and perpetuate rumors?

How is she blackmailing you with the email(s)? If she is threatening to tell your boss, you should inform your boss of the situation and let him/her handle it. Given your relationship with the boyfriend, you should have no involvement at all in the company's handling of the matter involving the ex. And, it's not a good idea to go around saying anyone should be fired.