Our pool is 15,000 gallons big. Yes, we generally heat it to 87 degrees, but I could keep it at 90 for a week or so if I was close to labor (like if I felt labor would be within a week or two). I also have an attached spa which I could heat up in 15-20 minutes to 99-100 degrees. So I could labor in the 89 degree water and hop into the hot water whenever I wanted. After I turn off the spa, then it flows as if it's part of the pool (it waterfalls into the pool when the spa heat is turned off)
To shock the pool after the birth, I would just pour in the appropriate amount of liquid chlorine (which is what we do weekly anyway) to kill anything left over. We do use algaecide occasionally (maybe monthly), rarely do we have to adjust PH, but we have chlorine stabilizer tablets constantly.
After birth, I could just leave the pool filter running for a couple of days, and keep everyone out for a few more, after a couple of chlorine shocks, I'd feel good about the pool being contaminant free and safe to swim in again.
With a smaller pool, it seems to be harder to maintain the proper balance (ph, chlorine levels, etc.) but we have our water tested weekly at the pool store and seem to do pretty well keeping it balanced.
Thank you so much for your perspective and the info, Apricot.

Maluhia!
Thanks Vanessa and Sweet Tart!