For what it's worth, I think you have a right to insist on her at least exchanging an e-mail with all of her boyfriend's partners. I believe that *everyone* in the relationship has to be comfortable with what is happening, including the other leg of a Vee. You are clearly not comfortable with that and that is your right.
You might want to sit your wife down again and talk about base rules. Some people even write those down and sign them, so there is no confusion. Your wife wishes for both you and her boyfriend to be in her life, which means she needs to make sure you are both okay.
I've had a similar situation in my Vee, when I told my (then) ex boyfriend that I would like to give our relationship another try, but this time in a poly set up. He had a very long hard think about it and agreed, but only under the condition that there would be no more than three in our relationship and he told me he was really only okay with our joint best friend coming in as another boyfriend. I was in a friends with benefits situation with said best friend at the time, although he had indicated that he would very much like to be more than that. Those were obviously fairly massive limitations and put a severe damper on what I imagined my immediate future to look like, however those were my exes rules and either I accepted them or the relationship wouldn't happen (either at all or as poly). We had to sit down together and figure out if there were compromises to be had and if we would all be okay with the limitations that my ex put down, but unless that happened the relationship could not go forward.
Obviously that is a more extreme example and your "demands" put much less of a limitation on your wife than my exes did, but I am trying to say that it is not unusual that every partner has their own rules and requirements and all of them have to be met (or compromises) before things can go forward in my mind.