Uhm, it isn't the family limit problem. (I think I should of put this in the first post...^^; )
I had a family of just a Wife and husband with one pet. The baby still wouldn't come out.
I know what you mean about the family limit. But even with the family above, the little message of 'a little bundle is on its way' shows, buy and build grays out, then the family just continues along their merrily way. All while the baby box is in the family selection area, the mother is still waddling, and the whole 'please choose a name for the little [enter gender here]' never shows up! D:
TBH though, I did try and play it out. But soon the evil baby stealer NPC started to complain on how the child was being taken care of.