Regarding a pregnancy in a logia user like Crocodile…
My headcanon is that the baby is actually only recognized by the fruit as part of the user during the first few months, but then there comes a point where the baby is separate from the user…
More than anything, it's that in a certain way and level, the baby gains willpower or consciousness (due to the stories that the baby reacts to stimuli the mother was exposed to during pregnancy), and it's at that moment that the fruit recognizes it as someone else…
Another way is that the moment the fruit user realizes the pregnancy, consciously or subconsciously, they recognize it as someone else and not as part of them, so the fruit reacts and stops affecting the baby.
There's also the saddest thing: the idea that logias can't get pregnant persists. If the Devil Fruit doesn't recognize the baby as part of the user in the early stages of pregnancy, it's possible that lodges won't get pregnant because they constantly suffer miscarriages when they transform their torso into the element. But beware, these are those so-called silent miscarriages, where you miscarry without knowing you were pregnant, giving rise to the myth that "female" logias become sterile, since male logias can have children.
Of course, this last one could end in a "miracle" with Crocodile, when he ends up not transforming his body for a few months and ends up discovering he's pregnant… It could also reinforce the Shishibukai's identity as a man in the eyes of the Marines or other pirates.
Well, this is my crazy mind and its obsessive ramblings.
I tend to go with your first suggestion as well. That the fruit does at one point recognize the baby as a separate entity with a will of its own, as you said.
I assume that in world, female logia users have been so rare that a misconception about their ability to have children could easily develop, whether it is because of miscarriages or because maybe the user died when not being able to transform. None of the male logia users we know of are confirmed to be fathers, so maybe the common idea is that logia, due to how it transforms the body, generally leads to not being able to have children.
(Both among the Paramecia and the Zoan are fathers and mothers.)
I think if you gave Vegapunk some incentives to investigate, he would find out that it IS a misconception (especially if you let the female satellites chime in with less of a male bias). He'd confirm that Logia users CAN have children, that they can even get pregnant.
(I mean, especially if he got his hand on Crocodile's lineage factor. Sure, he wouldn't be able to replicate his devil fruit but it seems like the lineage factor isn't just a person's DNA, but that it also contains memories and elements of personality.)
I'm always a fan of overthinking such topics within a fictional universe, it's fun!