I don't think you're being unreasonable. He shouldn't be going about "making a baby" when a baby is already on the way. And "I couldn't help it" is a terrible excuse. How much responsibility is he going to take for this additional baby if it indeed arrives? Are you expected to take care of both babies? It just doesn't make sense, and H shouldn't have gone along with it either.
Sorry you're in a tight spot, where there's no good solutions. I would think just about anyone would be "malcontent" if they were in your shoes. You'll just have to try to weigh what is the least stressful available road for you to take.
One thing to consider is that even after G and H have one baby, they may immediately go and make another baby. How many babies will there be before they can "help it?" Perhaps G should get himself snipped if he's determined to go down this road.
Sorry, hon. I don't envy your position.