Another death in childbirth.

Not necessarily in childbirth. The dates of their deaths puts the child after his mother. Most likely, the child couldn't be fed properly and likely starved without his mother.

That's exactly my point. If the mother died in childbirth (yes, that is the correct usage, if the mother dies giving birth or shortly after), the baby might have been given to a wet nurse, were one available (no 'formula' was available in the 18^th Century). Still, infant mortality was very high until between WWI and WWII; little William may not have survived under any circumstance.

What a heart wrenching sight. I teared up reading them.
Poor Mr. William. He lost his wife and child within two weeks.