No doubt that honesty is incredibly important. But in my experience honesty is the starting point - the starting point for discussions to increase mutual understanding.
For example, do you know what needs your gf hopes to have met by this new guy? Simply a chance to explore? Maybe a chance at marriage like you and your wife? Maybe some other need that a conversation might have elucidated - a need that if understood perhaps you and your wife could have met.
Having been that proverbial unicorn twice - I have some perspective. In one relationship, I was a full-fledged member of the family. We held joint bank accounts. It lasted nearly 2 decades and ended when one of my partners died. In the other, it was presented to me as if I would be a full-fledged member of the family, and one of my partners treated me as such, and the other began excluding so that they could be a couple.
Now, it could be that your gf really just wants the traditional marriage and kids. And if that is the case, sadly ther is nothing traditional about a triad. Nothing you and your wife could have done to change it. However if your triad, instead of being three equal individuals was in fact composed of your coupledom and your gf, that begets any number of stings, knowing you are always excluded at the core. Frankly, I found it unbearable.