One bullet in the torso or head would cause an instant and a gruesome death.
The problem is a shot gun only carries two bullets. However firing the first two bullets into June & Neville will put them out of action straight away. Avoiding the kitchen fight which caused Jeremy a lot damage.
A quick re load and there is a guarantee Sheila and the twins will die after one bullet each.
Shot guns are loud, but everyone would be in bed, sleeping, so would not have time to react.
If Jeremy was trying to avoid it looking like Sheila re loaded, then the rifle was a better choice. But as it happened he still had to re load the rifle. Twice.
It may have been easier to load a shot gun. Making it more plausible that Sheila shot everyone.
Jeremy could not give the story about shooting rabbits if a shot gun was used. But could still claim he saw a shot gun lying around that night which Sheila could have picked up.
Another advantage of using a shot gun, no silencer....
It is much more plausible Neville being scared of Sheila holding a shot gun as it is so powerful. He may not attempt to disarm her.
If a shot gun was not too long for Sheila to kill herself, do people believe this was a better option ?