Hi, I'm not sure if this fits exactly what you are looking for, but it's a manga about an obstetrician and his various patients.
http://www.mangago.zone/read-manga/kounodori_the_stork/
http://www.mangago.zone/read-manga/akkan_baby/ though I'm not sure if this is the one you are looking for
I recommend trying the manga "Delivery" by Ohta Tohko. Especially Ch.4! Seems to fit 1 of your requirement -
http://www.mangago.zone/read-manga/delivery/
Does anyone have a manga they suggest that has people working through miscarriages or trouble conceiving?