An excellent start.
The beginning was a little confusing, but I believe that was per design. It was all made clear as the story progressed. It actually was a pretty good way to start the story.
As a relatively new father myself, the story definitely tugs at the heartstrings. Big time. You did an excellent job of setting up an aura of tension and despair in the appropriate places. And the scene of announcing the birth had just the right elements of joy, surprise, and things-not-going-according-to-plan that made it entire appropriate for the world setting you have created.
I typically am not a big Angst fan, so it will be interesting to see if I can remain as totally enthralled with this story as I usually am with your other ones. But if you need to write Angst, then Write Away!
And a minor detail... in order to make the timeframe work a little more smoothly, you might want to change the flashback timeframes. It is unlikely Hintata can go from hiding "Morning" Sickness to giving birth in 20 weeks.
Author's response
Yeah, I caught the time frame mistake this morning when I woke up. Maybe I shouldn't wait until 2am to submit a story, huh? ;)
The angst will be minimal this time, but I listed it just in case.