Time of death isn't easy to calculate, and a post-mortem is unlikely to reveal the site of a tiny hypodermic pinprick, especially if Pfizer puts it (say) in between fingers, or where she's badly bruised. Things like that tend to be missed unless the pathologist is looking for them - and this is not to denigrate pathologists, but if you have a victim who has received serious head wounds, and then they suffer a stroke as a consequence (which I think this would probably look like), they're unlikely to do a minute body search for an injections site.
I don't know if Neckbeard will end up getting charged, but he's going to have a lt of questions to answer - the girl is black and blue, Catherine knows he's domestic tyrant, his children will tell the police that "Daddy doesn't like Mummy" . . . maybe he'll be remanded. Maybe TLR will find out about it and he'll be got at.
Have to say - am neither doctor nor lawyer so am making this up as I go along . . . a little knowledge. . . dangerous thing . . . blah blah