She may not have been shot 6 times all in one go, she had enough strength to walk around the room. Perhaps Sheila even received the first shot at this point which is why June walked around the other side of the bed? However, I'm not convinced that Sheila wasn't part of it, albeit in a (somewhat) passive sense.
June was shot 4-6 times in the bed. The only shot definitely not delivered while she was in bed was the 7th shot which was between her eyes to make sure she was dead. 4 shots were definitely delivered while she was in bed. The remaining 2 which were to her chest were delivered to her right side the shooter was facing her right side like all the other shots she received in the bed. Jeremy walking back into the room would not be facing her right side. It seems pretty obvious these shots were fired at the same time as the other 4 to her right side.
Both shots to Sheila were fired seconds apart.
It doesn't make any sense that he would shoot June 4 times then shoot Nevill 4 times as he entered (which doesn't work anyway because his left side would not be targeted in such instance, the bullet that grazed him is not where it would be if he was shot upon entering the room plus the trajectory of 2 of the shots establishes Nevill was not fully upright when those shots were delivered) then to let Nevill run away while taking the time to kill Sheila. He would have chased Nevill to try using the last 2 bullets to kill him.
This is basically what you are suggesting:
A)4 bullets on June in the bed
B)4 bullets on Nevill as he enters
C) Nevill flees
D) use last 2 bullets to kill Sheila
E) go try to find Nevill
F) fight with Nevill in the kitchen killing him
G) June stays in bed till Jeremy leaves then goes to Sheila to check her out
H) finishes killing Nevill in the kitchen and comes back upstairs to shoot June 3 more times.
June's blood was under Sheila's body that means June walked to the location before Sheila was lying there. Shooting June from the right side makes little sense if he came back upstairs finding June walking to the door. Her head injury was severe enough that she should not have been able to still be walking around when he came back upstairs and the evidence suggests she wasn't it suggest she was shot between the eyes when she was already down just to make sure she was dead.
The only thing that fits all the evidence is that June was shot 6 times. Nevill was shot 4 times then excaped and things progressed to the kitchen and Sheila either was dragged from her bed to the room or she woke up and was looking at her mother surveying the damage for a very short period of time before Jeremy came back upstairs.
Jeremy telling Sheila his plan in advance in order to try to get her to aid him makes no sense. He would not risk telling her and her then blabbing what he told her to her family. It would ruin everything if she did such.