It would appear that the boys were shot first, then the killer moved on and shot June. Ralph ran downstairs, but got no further. He wouldn't have called his feckless son - he would have called 999, asked for police and an ambulance, then, if he could, have run outside and alerted the farmhands. Sheila was still upstairs, terrified by the carnage, then found and executed. Badly. IMO.
What makes you think the boys were shot first?
I think they were shot first too, basically because they were not woken and in an undisturbed state, one was still sucking his thumb.
It's not a fact though, just an assumption.
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If true, why would somebody like Jeremy want to shoot and kill the children first?
Seems to me, that Ralph and June would need to be the first targets, and Sheila, because all of them would be a big threat to someone wanting to kill everybody...
Yeah I don't really know, put them in any order any it never quite makes sense, whoever the shooter is. 
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Yeah, but if you put the children at the start of this episode, it gives the impression that somebody did not want them being put into care, or being cared for by any foster parents - in my opinion...
That would be a reason why the kids might have been murdered first...
Well if we're just inventing reasons, then with a bit of thought any one of us could come up with a plausible story fitting either view.
For example, JB knew he had to kill the twins in order to be awarded the whole inheritance, but he actually didn't dislike them and knew this would be a hard thing for him to do, so he decided that he would kill them first, that way there's no going back and he wouldn't want to kill his mum, dad and sister only to find that he was unable to go through with killing the twins.
Or for Sheila, the children were the main subject of her berserk rage, so she went straight to the kids room, killed them, then had a moment of clarity and realised what she had done, it then enraged her further and she went off and killed her mum and dad, then inconsolable she took her own life.
It's all probably fiction, but the end result is the same, five people were killed.
We could probably come up with a half decent theory that the twins were killed second, third or last as well.