Here is a little more information on the arrest - turns out he does not have a concealed carry permit (according to WHNT). From what I can tell, no weapons charges yet, but if he became unruly, I would bet the Feds jump in with the 'gun free zone' laws saying he intended to do harm with the pistol.
The parent has been charged with public intoxication, having a pistol without a permit, and criminal trespassing.
Florence police say they will present the incident to the ATF for possible federal charges for having the pistol on school grounds.