This was an accidental discharge, noting that we commonly use the word, "accident" to include acts of simple negligence, along with random, unpredictable events. This may have been an act of simple negligence. However the facts indicate that she was doing what she could to do what she was doing safely, and in particular, being scrupulous about keeping the muzzle pointed in a safe direction. She made a couple of mistakes, first in the order of operations, resulting in a round being in the chamber unexpectedly, and secondly, attempting to remove the slide (requiring a pull of the trigger) instead of merely locking the slide back. But such mistakes coupled with adherence to the safety rules do not constitute "gross negligence", much less "recklessness".
Recklessness, in the criminal context, requires such a degree of indifference to life, limb, and property, as to constitute criminal malice. If she'd had the gun pointed at a crowd of people when attempting to unload it instead of down at the seat in the van, that would have been recklessness. This was not reckless handling of a firearm, it was careful handling of a firearm with a couple of unfortunate mistakes. If she hadn't been the owner of the vehicle that now has a hole in the seat, the owner could sue her for negligence, but this was clearly not a crime, and I think it was wrong to have charged her.
I have observed an increase, generally, in such charges around Virginia, which I believe is merely an attempt to "get guns off the street" on the part of law enforcement, since they always seize the guns and almost never give them back.