A lot of what you have written in this thread really echoes how I am feeling right now, even though our situation is slightly different. I have been in poly-esque relationships in the past and have been very involved in the LGBT community, but my DH (of 6 years) and our first shared girlfriend (of only 4 months) didn't even know the word "polyamorous" until I discussed how our relationship style has a name and how a poly community exists out in the virtual and real world.
Perhaps as a result of them being less knowledgeable about queer and poly issues and relationships (at least from a theoretical standpoint), I've been shocked at how little they communicate with me and each other about the rules and boundaries of our new triad. I was especially shocked a few weeks ago when she and I were chatting (from different countries), and she started waxing poetic about how she really really wants to get pregnant (she's very young and still in college) and has even sabotaged her birth control with recent past boyfriends to try to accidentally-on-purpose get pregnant. As you state, I am ABSOLUTELY NOT OK WITH DH/GIRLFRIEND HAVING A CHILD. I assumed that a young student involved with a married man would not want to get pregnant by him, especially without discussing it with him and me first! This was a powerful lesson about how explicit conversations in new poly relationships must be.
I am also struggling to dissect why I am generally a huge opponent of jealousy (I'm the one who slowly opened DH to the possibility of bringing another woman into our lives), but I am totally possessive over DH's DNA! Part of my jealousy on this issue arises from the fact that he has refused to have children so far, and I'm entering my early thirties. Unlike your situation, the fact that we don't have children yet would make it even harder for me to see another woman having his children. Also, I am on the point of going back to medical school, she lives in another country and has zero money whereas we have a small nest egg built up, and I am resentful that the two of them would throw their having a child at me under these conditions.
I can imagine, in the future, having a stable triad in which either I or a future girlfriend contribute the eggs/womb to have children with DH. As I wish to be a specialist or surgeon, three people to raise a baby, with me as the potential breadwinner, could be a great situation. But now's not the time. I'm very hurt that they didn't think to discuss this situation, and, although they were using condoms (in threesome and twosome scenarios), her admission to desperately wanting to have babies very soon scares me.
When I tried to talk with them about it, I felt like they ganged up on me, claiming that they used birth control so I was worried about what was really a small risk. But she also is adamantly against having an abortion herself, and no risk is acceptable to me. The past few weeks have been really difficult because we all have our (previously secret) demands... I don't want them to have PIV sex since she would not consider an abortion. She doesn't want to have an abortion but wants to have PIV sex. She could accept not having PIV sex with DH because she could get it from other male lovers, but he doesn't want her to have sex with other men because of security/jealousy issues he has.
Like you, we've finally hashed a lot of things out through lots and lots and lots of discussions, in which all three of us have gotten hurt, but we have finally been honest about each of our personal limits and needs. When they realized how devastating their having a child would be for me, and that it would likely result in me ending my marriage with DH, they decided that they would avoid PIV sex for now rather than hurt me and possibly ruin my relationship with both of them.
Meanwhile, I have been having private discussions with DH about his jealousy issues and have encouraged him to open himself up to the possibility of her having protected PIV sex with other men since I feel terrible that DH and I have PIV sex and she does not. That seems really unfair to her. Through our discussions, I realized that one of his fears is that if he okays our GF's sexual relationships with other men, that I will demand to be with other men, as well. I have wholeheartedly reassured him that I respect his needs and insecurity about me being with other men and that I would never demand that he open our relationship (between him and me) to men just because he opens up to our GF having another guy. Now, he's reconsidering his limits about her having male lovers.
Our GF seems to be head over heels for both of us, but I don't want to control her or mandate what relationships and sex life she must have. She is the type of person that is easy to manipulate and convince into doing/not doing anything, but I think it's disgusting to take advantage of her compliant personality by forcing her, for example, to agree to an abortion. She's already used the "L word" (awkward!) and talks about the three of us in the long-term, and has already come out to tons of friends and family about us. (Whereas DH and I see our triad relationship as a more casual dating thing!) My DH was convinced that the prohibition of PIV sex would send her running, but she accepted the condition with grace and understanding after several heartfelt conversations. But I feel guilty, too, because if she reeeeeaaaaally wants to have a baby soon with someone in love with her, maybe she's wasting her time with us as we aren't looking for that right now.
Sorry to maybe hijack the thread with my story, but it was so comforting to hear that other people are in this thorny situation and struggling with what to do. At least this issue has made my two lovers better communicators, even if I kind of forced them to be...