Gronky any tests done on the child are part of the child's medical records. No mother can withhold that permanently. (She may not tell her child while it is small, but once the child is old enough to access their own records they could find that out.)
I do not agree with any of the pre-pregnancy arguments or the arguments about the rights of the fetus outweighing the rights of the mother. Once the child is born, and has actual issues, whatever is then uncovered about perinatal issues in the search for answers, detailed assessment or treatment considerations is rightfully part of the child's medical records.
However, the notes about previous pregnancies, abortions, miscarriages, births or stillbirths are only of actual use to the obstetrician caring for the mother. Hence they should not be a normal part of the child's medical records. There should be a separate mechanism by which one may apply to see this information, with the mother able to refuse as this is her confidential data and her medical history, not the child's. No consent, no disclosure. There may be exceptional circumstances, such as twin births etc, but the decision should be made by a legal department not by some data recording company.