This is very intriguing.
Trying to work out who did it, why and how it was supposed to work.
I don't think they have the results of the toxicology report yet for the contents of the injections.
There appears to be an assumption that it was a sedative .
Did we get an actual cause of death for the mother?
We know that the father had serious smoke inhalation and almost died
Are we supposed to assume that his wife and the girls die from smoke inhalation?
The girls locked bedroom looked untouched by the fire so did they die from smoke that seeped in?
As well as the question of who did it there's also a question about the method.
For example if someone planned to kill the girls was the plan to sedate them then lock the bedroom door so that the fire likely wouldn't get to them but they would die from smoke inhalation?
Unless either the father, mother or both were actually administering the injections then I can't see them allowing themselves to be injected by someone else- at least not without a struggle.