I don't even know whether "her grandmother's candy store" referred to her father's mother, with a married name of "Aird", or her mother's mother. So the family-legendary candy store that dated back to the mid-1800's (my grandmother was born around 1890) will never likely be tracked down. But the recipe remains, as good as ever. The ingredients are very ordinary, but I've tried to add some explanation of the delicate business of boiling down the mixture and making proper fudge.
The sugar and fat in fudge have a delicate relationship. Overcook fudge and it will "set" right in the pot, or crystalize into a sludge of sugar grains sitting in a thick, semi-fluid, amorphous goo that bends but doesn't break. Many commercial fudges are what I call "sludge".
Real fudge "Sets", and can be snapped in two. It's just tricky to make fudge, I remember my mother having many failures despite making it almost weekly the whole time she had three boys growing up. Even failed fudges still taste good, it's hard to go wrong with sugar, chocolate and butter. But making a great one is like having a perfect ski run or golf shot. Best of luck.
Combine and heat together in a saucepan, medium heat; stir constantly, scraping sugars from sides of pot. Stop stirring at once when it boils.
Lower heat if it boils up to top; heat can be increased a little after some fluid boils off (but don't go to "high" heat).
If you have a thermometer, it's cooked at about 114C - simplest to remove instantly when it hits 115C. (This is in Calgary at 1080m elevation, it might need another degree or so at sea level.)
The way to calibrate is to go back to the old test:
Dip spoon a bit into cooking mix, drop a bit into cool (not really cold) water, reach in and form it into a ball. When you can make a "soft ball" of the candy, that just barely holds its spherical shape under its own weight when placed on the counter, it's done.
Remove at once, place whole pot in sink.
Add 2 Tbsp. butter,
1 tsp. vanilla
BUT don't stir in, just let them boil away on the top of the candy while it cools for several minutes. At about 60C, i.e. when you can hold the bottom of the pan to your hand without snatching it away:
BEAT THE CRAP OUT OF IT. Just WAIL on the stuff.
Hold the pot in one hand, then use a wooden spoon and beat quickly with strokes that go a quarter of the way around the pot, fast as you can. A major wrist and arm workout and you may have to switch hands a few times.
When either the mixture STARTS to feel like it is thickening, or when it STARTS to lose its gloss, IMMEDIATELY start pushing the rapidly setting fudge into a greased pan.
For extra points, have a handful of chopped walnuts and raisins ready, and when you get so you can spot the signs of setting early, toss in the nuts & raisins for the last dozen beats to mix them in.
Allow to nearly set on counter, then score deeply with a knife and put in fridge to finish.
Consume when you can no longer stand the suspense.