I second (third?) the notion that electronic communication is not private. I "snoop" on my husband's phone (idle curiosity, not checking up... he hates texting so there's never anything interesting anyway) and while he doesn't bother with mine, I wouldn't care if he did.
My girlfriend and her husband share a cell phone, so I assume anything I send to her might get read by him instead. They also have a teenager, and teenagers are notoriously snoopy.
For me, it all comes down to "honesty is more important than privacy" in a relationship. We don't keep secrets. Oh, there are things we don't bother telling each other... usually little guilt things, like I went on a shopping spree and wasted money, or he started smoking again when he was trying to quit. Usually things more about embarrassment than secrecy.
As for the flirting, I'm with Jayne on that. Not in that I'm a hopeless flirt (teach me, Yoda!) but that I think each person is responsible for setting out the boundaries of their personal situation. If this girl and your husband have history, then I can totally see how it would be acceptable to her to try and pick up where things left off.
I also find it ironic that on one hand you're pursuing nonmonogamy, yet still holding others to the assumed expectations of monogamy. It's the second time this week I've seen a woman get upset for some other woman hitting on her husband, on the basis that she should have assumed he was in a monogamous marriage. "It's not that she was doing it, it's that she thought it was OK to do it." *shakes head in confusion*
“As I am sure any cat owner will be able to tell you,
someone else putting you in a box is entirely different
from getting into a box yourself.” —bisexualbaker