It's her decision, of course. (All you can decide, ultimately, is what you can live with and what would be a dealbreaker to you.) In general, though, it just would be a wise thing for her to do to at least tell her "other dates" that you're in the equation. Otherwise, it's not honest, and that's not ethical, plus it can lead to some really bad drama somewhere down the road.
There's all kinds of "shades of poly;" it's not always done in a certain way. But 100% honesty (with all parties involved) is usually considered a must. In your case, I think maybe you're wanting to meet whoever she's dating in person, which is actually a pretty good idea and advisable in most cases. That way, everyone has direct confirmation that "the other person is okay with what's going on."
All's I can think of to tell you is to try to engage her at a time when you and she are both relaxed and able to discuss things calmly. Try to avoid lines of conversation that try to establish "who's wrong or right;" instead just tell her that you'd really like to meet the people she's dating, and is there some compromise you could come to, or some way to make that work. Tell her you don't mean to snoop or control, that this is just something that would make the arrangement easier for you. Try to give her ample chance to express her feelings, and show her that you are listening to her and hearing her.
Beyond that, I think it's kind of up to her to be agreeable toward you, and at least try to come to some kind of a compromise. It's not like you can just "cause her to be agreeable;" she has to make her own choice about that.
But yes, I would advise being open with all involved parties about what's going on. If she doesn't tell her dates about you, it's almost like she's cheating on her dates. Not that I'd *say* it to her like that, but. Maybe she doesn't realize what she's asking? I'm a huge proponent of freedom, but responsible behavior is still important as well.
Anyway, sit down with her for a heart-to-heart about these things as soon as you can.
Love means never having to say, "Put down that meat cleaver!"