Sounds very urban legend-ish or tall tale-ish.

Imagine a two year in or out of a car seat.....actual taking hold of a weapon....fiddling with it.....and somehow or other being able to hold, grip, point and pull the trigger....all maybe not in that order.

Most pistols are too big for their hands to be able to do much of anything.
Most pistols would have a 6-7 pound plus trigger pull....the span of the hand to reach the trigger while holding would be impossible.

now think of a little two year old sized hand being able to overcome all the above......

Possible? On a yes or no scale only......yes.

Probable? with the odds on the eighth decimal point of one percent....NO!