At the shooting range,

[Bassim]

I am wondering if my sentences are grammatically correct.

At the shooting range, the instructor became enraged as he spotted the woman inadvertently turning her gun in the opposite direction of the target. "Do you want to kill us all?" he yelled, diving for cover.

 

[teechar]

turning her gun in the opposite direction of the target.

That doesn't work. Try:
"swinging/pointing her gun in the wrong direction."

 

[SoothingDave]

It's supposed to be pointed "downrange" if loaded.

 

[andrewg927]

It should be "a woman" instead of "the woman".

 

[emsr2d2]

"the woman" would be OK if she had already been mentioned in an earlier sentence. For example, "A woman caused chaos at a shooting range yesterday. The instructor became enraged when he spotted the woman ..."

 

[Tdol]

How about away from the target?