The test is not :conclusively prove” nor is it “beyond a doubt”. The test for proving a crime is “beyond a REASONABLE doubt”. I find it a bit hard to see what was the REASONABLE doubt.
I don’t see it that way.
The kid could have drowned.
The kid could have had an overdose of chloroform.
She could have killed the kid.
The grandfather could have been involved.
Etc. etc.
NOTHING to directly link her to the killing of her child.
All vague circumstantial evidence and LOTS of “reasonable” doubt and if I were sitting on a Jury, I would NOT convict ANYONE of a capital offense unless I was sure beyond a reasonable doubt they were guilty and this was not the case here.