You can't force your wife to change her mind about talking to her new friend, and I don't know of any magic words to say that would convince her. I think she is going to have to learn on her own that holding back on communication just causes a powderkeg to go off later on down the road.
I think you should make it very clear to your wife that you think her friend should know more about what's going on. If you've already done this, then you've basically done your part.
Good luck and I hope things smooth out.
Love means never having to say, "Put down that meat cleaver!"