Neville would not have " jumped on Sheila "
He'd have initially given her a wide berth not imagining that she meant business while she had hold of the gun. No doubt he tried to talk/reason with her as any father would do with a daughter who was making threats.
Talking is what anyone would do to those on either the brink of suicide or such as in Neville's case. Show aggression,and it aggravates an already volatile situation.
You're forgetting that Neville was an educated man--not a thug.