If you're going to successfully someone's love you're well within your rights to know what's going on. Then you need to set some ground rules. There's no rule book. The degree of openness or privacy is whatever you all agree on. Sneaking around behind someone's back about things the other lover should know about is definitely wrong and will ruin the relationship, but that being said there is the need for some privacy with a lot of people.
For example, I don't need to know the details of what my SO does when she sleeps with her girlfriend, and frankly I'm not curious about it - it's their business. I do want to know where they're going and when they should be back in case something happens but beyond that I don't intrude. (It helps that her gf is a good friend of mine)
You certainly need to have your feelings heard and some sort of resolution. I hope you can work something out.