Firstly I would urge you to reread gala girls post because I think she has summed up my reaction to your story perfectly
For myself, I am the newest member in our triad however we have a long history. And we haves all children involved, which changes the dynamics hugely.
For me,yes I need to be kept in the loop. All three of us live together, I like to be aware when they are simply in shitty moods as well as when there are issues.
Take this week. Both of them have been fighting because a parenting boundary was broken - the fact that it was a child related issue (and biologically the kids aren't mine) meant that the issue didn't need to involve me. And I didn't want either of them venting to me as such (I hate feeling like I need to pick sides) but I needed to be kept informed of where they were at. Speaking/not speaking/angry sex, whatever.
I couldn't be in a triad where I was treated like I was less deserving of the whole story. We either make it work as three people (which means constant communication. Even if it's just to say "hey, I'm a grumpy dick today - leave me alone for now". ) or we change the rules and go back to a different set up.
Our FMFTriad + 3 children + 2 pets = one crazy household