Sounds like you are going through some growing pains in the beginning stages of your relationship. It isn't uncommon. There doesn't seem to be as much in mono relationships... you get together, you hang out and everything falls into it's pre-determined place as laid out by societal norms. Much easier.
I agree with superjast in that he lays out my experience with labels such as primary and secondary. As time passes they lose their strength and fall by the way side and become what you are saying, everyone brings their own uniqueness to the situation.
Mono has posted before what Eugenepoet has said. He very much thinks the same way. I could not be with Mono without having my husband in my life as well. Because of the negotiated boundaries we have in our relationship, we really are all meant to be together. This came with a lot of time and a lot of work. We had similar discussions, long emails, long talks, heart in throat moments..... it was hard work, but eventually we talked it all out and came to the end of it all. To a place where we just understood each other as no one would unless they had gone through some difficult communication together.
I would hope that you stay patient and hopeful. I would hate to see you break up over the whole "primary/secondary" debate.... cause really it means nothing later on, what you create is your own with them. It will be like no one else's life and you can make it what you want....
Maybe re-defining the terms to make them your own would help. With them of course. We seem to of. To us, primary means the one I get to spend more time with, and secondary means the one I don't get to see as much. Full stop, end of story. The rest we blew off because it didn't fit.