The first shot was instantly fatal. Thus no need what so ever for the alleged killer to fire at someone already dead. After all 'forensics is not your thing' 
Hmm, but psychology IS. SO, I don't believe for one moment that Sheila was psychotic. There was NOTHING in her behaviours to suggest such, ergo, HAD she shot herself once, and missed, with the injury she'd inflicted, I don't believe she'd have been capable of doing it again. However, I can quite see that. if she wasn't ready to be dead, she could easily have moved as Jeremy took the first shot. Maybe moaned slightly. WHAT was he to do. He could have left her to bleed but he couldn't guarantee how long it would take. He didn't know the wound was mortal, ie not instantly fatal. It was very inconsiderate of her not to die. He had a dilemma on his hands. He couldn't just leave her so he had no choice. If he wanted to pass it off as suicide he couldn't strangle he. He HAD to take a second shot. Not perfect, but he got away with it for a month.