Welcome to the boards.
Just to be technical, you had a MFM vee relationship, as you report being straight, which would mean no romantic involvement with the other male.
It's up to you to figure out the source of your discomfort. What, exactly caused the discomfort? Is it that you feel you lost something? Is it that you feel she's gained something that you haven't?
One thing to keep in mind is that a new partner for one person isn't necessarily going to be a partner for another. Alongside that, expecting anybody you get involved with to get involved with you as a couple, instead of you as individuals, is a dicey proposition.
As a straight couple, any other person getting involved is necessarily only romantically involved with one of you. There's nothing wrong with that, certainly. It doesn't appear to be working well for you, though, as she's getting additional ties and you aren't. The obvious answer to that is for you to find another woman to get involved with.
Prior to doing that, though, it would be a good thing to sort out the issues you're dealing with and then communicate what's going on clearly with the other folks it will affect. You have to understand exactly what it is you need and what your wife needs and so forth before you can figure out exactly what to do.