Other possibilities:
Gun was out of ammo or jammed
He didn’t know how to operate the gun
His natural aversion to killing took over once he thought the son was neutralized
He was overwhelmed with adrenaline and wasn’t thinking clearly
yes. your options may be the more reasonable ones.
I think he was probably afraid the police would shoot him seeing him with a gun, and when he realized that, he dropped that gun like a hot potato. Smart.