All seems quite straight forward to me.
The twins may have slept through the kitchen fight etc. I would have shot the twins after Neville & June as they posed less threat. Why couldn't Sheila have slept through it ?
As mentioned, Jeremy could have put the gun in the bedroom. Gone to get Sheila & said 'mummy needs to see you in the bedroom'. As soon as she enters the bedroom she is pulled to the floor & shot, which would only take a few seconds to do to an unexpected Sheila.