Just because everything happens in the vicinity of the stomach doesn't mean the stomach has anything to do with it.
The umbilical cord carries one thing to and from the baby - blood. Oxygenated blood through one vein, and deoxygenated blood and waste through two arteries.
Nutrients are carried to the baby in the blood, just like they're carried throughout our own bodies (and you thought blood was only for oxygen). Anything that can be absorbed in the blood can be carried to the baby. It's the placenta that does the heavy lifting during the exchange of oxygen and nutrients between the mother and baby. It acts as a sort of filter, making sure that mama and babies blood never mix, as well as preventing exchange of some substances which could harm the fetus.
Not all substances are filtered. Many drugs pass right through, which is how babies can be born addicted to drugs. Neurotoxins, heavy metals in vaccines - it all depends on the compound. I'm sure someone has made a list of known compounds - but I'll leave that to you to research.
It's super fascinating, and well worth understanding if you plan to have children.
