I just re read this thread and noticed both of these women are your exes (sorry, I just woke up and the melatonin is wearing off!) so I can see why she may be upset. Exes are exes for a reason. However--she needs to respect your privacy. If all you said was honestly business oriented and that is it, she shouldn't be too crazy upset. She should be thankful that you were honest, upfront, and the emails were honorable.

I would talk to her about it with something along the lines of, "I understand why you're upset, because of your past relationships. However those emails were strictly business oriented was all. You're the one that I'm with, and the one that I want to be with. However I feel slightly disrespected that you didn't come to me and ask me personally about what was going on. I feel you don't respect my privacy" something along the lines of that.