Why isn't the child a part of her body anymore? Because the tyke isn't enveloped? How does this logic apply to other things that can be enveloped? (bombs, contraband, small animals..)
This is a really stupid argument, I don't think you can honestly believe it works. When an embryo or fetus is within the womb it's entirely dependent on the mother's blood supply for survival, just like all the other parts of her body and unlike those silly examples you're giving. If it's something that is using your heart, your lungs, your blood to survive then it is part of your body (if you're about to respond with some stupid parasitic example: yes, I have no problem with people removing parasites from their bodies). This is obviously not the case after the baby is born, the umbilical cord can simply be severed and the baby will survive without relying on the mother's organs.
So I'm gonna ignore the parts that basically say "I'm right just because" and the parts where you completely ignore the argument about birth not altering anything about the child itself. But riddle me this: Right before birth the baby is obviously no longer dependant on the mother's blood or organs for its continued survival. Are you arguing that it's not a person simply because it is inside of her? Because then there's plenty of innuendo you need to address...
It does not matter whether it's a person or not. That's the whole point of the bodily autonomy argument he's making! Let's say, for the sake of not even bothering with this red herring argument, that personhood begins at conception. There is no need to clarify when somebody is or is not a person for the sake of this particular conversation.
Now, given that that's the case, we have the rights of two people to consider. When that happens, you don't generally pass laws imposing medical rules on the one for the sake of the other - the exceptions that make it "generally" instead of "ever" occur only when the imposition on the one's rights is so small, and the benefit to the other is so large, that there's no meaningful question. You don't mandate people with two functioning kidneys to donate one to somebody in need. But let's go further! Let's take the example of somebody who
does agree to donate one.
You don't let people be imprisoned for negligent homicide if they (to use an example as convoluted as some of the ones I've seen) sleep through their alarm, miss their appointment for the surgery, and the recipient dies in the meantime while it gets rescheduled. You don't let them get sued if they lose a kidney to a vicious mauling by their pet crocodile. If they got drunk and wandered into traffic, an accident might be ruled their fault, but they aren't going to be compelled to donate the organ anyway if their kidneys are damaged in a way that makes it unclear whether or not they'll be able to survive with just one.
Yet here we are, needing to argue whether a woman in basically similar scenarios ought to be compelled to undergo serious medical procedures against her will because of the child's rights, or punished for failure to take adequate care of her body for the sake of the child's rights, as though we as a society do this in any other sphere.