plainpain, I can't imagine what you're going through. As a mother that did the co-parenting thing, I have to agree that thinking that for 18 years the two of them won't speak is probably not a reality based thought. Things come up with kids that require discussions, not just 'have her home by 7' or 'where will he spend Christmas?'. There are problems that need a conversation. There are school functions, school meetings, sporting events, etc. While it is absolutely horrific to imagine, I think at some point, if this is his child, they will have to begin speaking.
For now, I would do nothing. There's no need. She's still pregnant, so it doesn't matter. When the due date is near, start checking her local paper for the birth announcements. If it goes 2 weeks past the due date, have an attorney contact her.
In the interim, I would speak to a family counselor to see what suggestions he/she has about situations like this. Try to find one with experience.
Are you planning on moving back to the area that you were living in before? If not, beyond sending a check, co-parenting is going to be next to impossible. No mother, even an OW mother, is going to send her baby across the country to stay with a man that the baby doesn't know, and where there is a woman (you) that the mother doesn't like. You're a mother - you know this. So either the relationship with the child starts when the child is in the 3rd or 4th grade, or the locations of the two parents are going to have to be a bit closer.
Have you spoken to an attorney yet about protecting your children in the event that you and your H separate? If she's already gone to court for child support, in some states she'll get more because she's now 'first in line' regarding demanding funds. Also, if you are working, the courts may look at your income as 'available' income for child support. It's happened before. The courts would take your income and your husband's income into account when running the calculations, not just his. Yours will definitely factor into the basic needs requirements, so she'll probably get more just because. You'll want to see an attorney, and soon. Sadly, you may be better off financially if you and your H are no longer married. That doesn't mean separated, but not legally married. A lawyer can answer these questions.
And I agree completely - the folks in 'I can relate' are always so helpful. They've walked this walk already, and can provide invaluable advice.
I'm so terribly sorry for you plainpain. I can't think of anything more painful than knowing that the OW is going to be around for 18 years. You're stronger than I am. I don't know if I could handle it. Just take care of you and YOUR babies, like I know you already are.