Personally the only time I had an issue with Dh going out with friends close to my due date was when I knew he was too far away to get home in time, or if he couldnt get home. Other than that, life went on as usual until I went into real labour and we had had the baby. But then after giving birth, I actually didnt mind Dh going out and having down time with friends.

It does sound like you have deeper issues with this friend. Ok so since having DD they have baulked at the idea of being around kids, but things do change once you've had kids. Some people dont feel comfortable being around them. My Dh was the same with other people's kids, we would cancel things so that he didnt have to interact with the kids, if people came over it was a kid free event. But that was because we werent in that space, and also kids freaked him out.
If you have an issue with them, then explain it to your DP. Its really the only solution.