Although you not address that question to myself, I noticed, nor have received reply to my own brief question in regards to "mixing" of blood asking "precisely when?".
The exaggerated "every drop" coming from the idea of Christ's humanity deriving from Mary(?) which has *some* merit, but for reason of medical knowledge needs be constrained to consideration of fetal nourishment systematic, for the egg itself is but potential for production (not to be confused with capital "C" Creation).
The egg, upon fertilization, never directly shares circulatory systems with mother. For those interested http://www.uptodate.com/contents/placental-development-and-physiology tells it better than I myself can, and this graphic (also available in larger size http://en.wikipedia.org/wiki/File:HumanEmbryogenesis.svg) possibly helpful;
Medical proofs indicate the two blood circulatory systems being distinctly separate, leaving basis of possibility (not guarantee) of there being some slight mixing of blood, at birth, from infant to mother, with that contingent upon there being some injury to the mother, a breaking of the skin of the mother with possibility for some slight re-absorption of blood, precisely there.
So much for the "passing through like glass" imaginings. Can't have it both ways. Natural childbirth for Christ? What ever on earth or heaven be the matter with that? Theologically speaking --- natural in all ways other than means of conception, is not only the wisest choice, it is the only choice...well, other than "Hark! The Herald angels sing" (to the lowly shepherds) and the Magi seeing the star and visiting, etc.
He was born much as most all are or were, with the significant difference being the conception, not the birth itself.
Otherwise, I take it there can be fetal cells (not of blood) which can remain in a mother for some. This cell transfer uptake coming through the maternal side of the placenta in the same manner fetal waste product be taken up into mothers own NON-blood circulatory connection to placenta --- and if memory serve this being more enduring in regards to cells from male fetus to mother, than female fetus to mother. Though I have no link for news item in popular press conveying such information, something to that effect I do believe surfaced not long ago.