BeSha'ah tovah!
The time to induce the childbirth is really a medical decision and thus not affected by the potential of having a
brit milah on Ta'anit Esther. In such a case, the father,
sandak, and
mohel eat the
seudat mitzvah after the
brit. The mother who just gave birth is
exempt from fasting on this minor fast and may also eat. The
seudah for the rest of the guests is pushed off to the evening.
Whether the doctor breaking the waters brings on
niddah status is a matter of dispute. Our rabbinic supervisor, Rav Yehuda Henkin, holds that it does not make a woman a
niddah on its own unless there is attendant bleeding.
For all procedures that enter the uterus, the
size of the instrument that enters is also important. Instruments larger than a certain size render a woman
niddah even if there is no bleeding. Opinions as to this size vary. R Henkin rules that an instrument with a diameter of 19mm or more would make a woman
niddah.