According to the letter, Jeremy loaded the rifle and Sheila shot June and Nevill, attacking Nevill in the kitchen when he was badly wounded, no mention of who killed the twins just that Sheila wanted to be with them and begged Jeremy to shoot her, which he did. So he only admitted to shooting Sheila and blamed her for shooting June and Neville.
So Sheila was capable of using the rifle and beating her father (without breaking her nails

)- and what was the story for the lack of prints on the rifle .and how did the silencer get in the cupboard and why use it?