OK, in no particular order...
I think it being long distance probably makes it harder. It's not just that there are other people, but also you're not there, meaning that A) you have no clue what's going on and no control over it and B) you can't be with her yourself, so her other partners enjoy something you don't get to.
Not knowing can be harder. An unknown can be scary, knowing the people and what's going on can be very relaxing. Do you talk to her other partners? Just talking to them a bit might help you. They're obviously important in her life and so getting to know them is probably a good idea.
She shouldn't reveal things that her other partners don't want repeated. However you could have a talk together (all of you, or any combination that makes you comfortable) to see what they're comfortable with sharing or not. Explain what you want to know and why. Explain you don't want to intrude on their intimacy but you want to feel like you are part of her life, and since you can't be there with her, the only thing you have left is hearing about her day. (I might be projecting or extrapolating here. If so, substitute your actual feelings).
Do you know why she has a don't ask, don't tell policy with you? Obviously she knows her girlfriend has that other partner. Why doesn't she want to hear about it if you do?
Right now, it seems like they have a close bond and are together, and you're the odd one out. As much as she said she'd pick you over the rest if you said so, it seems to me she said it to comfort you that she cares about you, but it would be heartbreaking for her, and might not be realistic.
Try and talk to her about how you feel. Don't make it a blaming game, just try and explain your position, and that you want her to understand how it feels for you so that you can work it out together, the four of you.
It's good if you don't feel cheated, but she did lie. She lied about how many partners she had, and she hid the fact that there was another male, which is often important to guys.
She did come clean and that's good, but you need to understand that maybe it is harder for you because she did lie. Because you might be afraid she will do so again. Because it would be so easy in this specific situation. If that's the case, then I think you should tell her that as much as you appreciate that she told you the truth in the end, you need her reassurance that she won't lie about these things anymore, and that she is sorry she did in the first place.
Maybe that could help you.