"...so Mary fed God, and heart the beat of God's heart."
According to medical science, mother and the fetus do not share the same blood. There is a barrier (by deliberate design, we would likely agree) which precludes that from occurring directly.
Otherwise the ties between mother and child are quite strong in many other ways. We may not know the half of it.
Recent findings indicated that tissue, or cells (bodily cells -- I'm not sure which, perhaps skin cells? I don't recall which sort of cell, or if there could be more than one type) were claimed to be taken up and absorbed by the mother, and remain within her own body for years after giving birth, with those of a male fetus said to remain longer than from a female, with these cells from child to mother lingering many years altogether, if memory serves.
If that same memory further properly recalls (near enough) this taking up of bodily cells is something of a one way street -- from fetus to mother -- but very little or nothing the other direction?
But none of this 'circulating the same blood' talk (which you didn't say-- or perhaps do know better than) as in the same blood circulating through the heart and body of Mary, and Jesus as fetus, and his own heart -- then back to Mary, then again back to he who would be the Christ.
Medical knowledge says that not at all likely in normal human development, being that even small amount of blood leakage across the membranes which separate as part of the placenta(?) which functions as two-way exchange interface -- but not quite comparable to being "filter" per se other than for passing nutrients and oxygen, but not blood directly, could be hazardous for the fetus.
Though blood does not pass or flow directlythrough both circulatory systems, being as they are kept separate, the passing of oxygen on to the fetus --- entails the mother breathing --- and that oxygen when dissolved in her own blood then passing on from being pumped by her own heart to the placenta, so that portion of the physical breath of life (oxygen) comes from nowhere except through the mother first, along with nutrients (and possibly water molecules?)
It's something along the lines of the fetus being it's own self contained life from it's beginning formations, and in the 'sac' which develops shortly after implantation, with the later developing fetus all but fated to being sensed as intruder by the mother's own immune system -- IF not for some cellular/chemical trickery as it were, but which considerations taken all together (beyond my own sketchy and probably somewhat erroneous descriptions) leave the fetus, from near hours of implantation on uterine wall, first forming it's sac which shields it from outside intrusions, other than by connection to the placenta which itself begins formation almost simultaneously with the sac.
I do not recall the more precise details in how the masking of "foreign element" of the fetus functions-- but this sort of thing taking place possibly at the placenta(?)
There are better sources online for explanation of course, but to change the subject a bit --- the medical evidence rather blows away the portions of "pro-choice" abortion issue argument, where a woman claims that the fetus is her body. Uh-uh. From implantation, from medical perspective -- that foetus once it begins growth from blastocyst (or a bit before? shortly after?) is it's own life form, though admittedly utterly dependent upon womb & mother.
Which would well enough leave the pro-choice'ers needing change their argument to "IN my a woman's body" from the more stridently proclaimed "it's my body" to more honestly reflect the medical truth that a foetus, in regard to the mother's own circulatory systems -- IS a foreign life form, which means boys and girls -- the fetus is not the mother, long before that same becomes born. This has implications...
Actually I do know something about embryology and fetal development. So I'm a little unclear about why your post started with a quote from mine.
But certainly the fetus is a distinct being from the mother. We know this from modern genetics, but even the mistaken embryology of Aristotle and the early Scholastics never identified ontologically or any way but materially the fetus with the mother. The dam, they thought supplied the hyle, the ‘stuff,’ of which the child was made, while the sire supplied the quiddity, the what sort of animal it was.
In any case the Chalcedonion definition of two distinct natures in one hypostasis survives modern genetics and embryology. So, if we understand IHS to be both God and Man in one person, and Mary was the mother of the one person, the we have Mary Theotokos and Deipara and Deigenetrix.
As to the criticisms made of Mariological teaching, every last one depends on graces bestowed by God — something that you'd think would be well received by our antagonists.
