The links in the opening post are not working at the moment, however, when I did manage to see the NtK it appeared to be PoFA compliant, which means that if the driver is not identified, they can transfer liability to the keeper.
I cannot really see any defence to this PCN. The driver parked in a disabled bay without displaying a valid blue badge. You even admit to going inside to make purchase whilst waiting for your son to use the bathroom.
On what basis do you think you can appeal?