I think the children were shot first, simply because of the risk of them waking up and running around would make it more difficult...
Shooting June and Nevill would run the risk of waking both the twins and Sheila.... 
The silencer was used on purpose to mitigate the threat of people in other rooms waking up during the shots.
What would be worse waking the parents and having them confront you after you expend a magazine on the boys or the boys waking up and running around after you expend a magazine on the parents?
Shooting the boys first and risking the parents waking makes little sense and moreover had that happened then 10 shots would not have been fired into June and Nevill in the bedroom because the gun would not have been fully loaded at that point.