No, double coated dogs should never be shaved (except when medically needed--like my poor german shepherd)
The Golden's double coat acts to keep her cool, when she's shaved the coat is undercoat which is NOT designed to protect against the sun.
The only areas that can be 'safely' shaved are the areas that are undercoat, so back feathering can be taken down, belly hair can be taken down. I used to do a cut on a golden who got hotspots every summer if we didn't do it and what we did was shave the belly, trim all feathering to roughly 1/2 - 1" in length and trim under the ears short and keep chest hair short. The owner noticed she seemed cooler and didn't get hotspots as her coat was always kept nice and thin.
The best thing your dad can do is either take her in to a groomer nad get her undercoat stripped out, or purchase an undercoat rake and just keep brushing.