Another strange factor is the location of Sheila´s body (somewhat unrelated to what we are talking about here.)
Why would Jeremy place her in June and Nevill´s bedroom on the floor, why not in her room, why not in the twins´? If he wanted to stage a believable suicide, why on earth choose that bedroom? Makes no sense, not as if it had been planned to look like a suicide.
You can say the same for Sheila, why did she choose that spot (I realize others think she died elsewhere - I don´t).
I have some thoughts on that, but I will refrain from wild speculations!