Your great grandma didn't use corn syrup in her caramel apples, and neither should you! You will find all kinds of recipes for caramel and caramel apples, and basically all of them say that you need corn syrup for one reason or another. What you need is something sweet that has a similar composition of glucose and fructose as the corn syrup. Corn syrup is about half glucose and half fructose. The corn syrup you buy at the store is usually Karo brand syrup. Karo is a mixture of half corn syrup (100% glucose) and half high-fructose corn syrup (90% fructose). Giving it about a 50/50 mixture of glucose and sucrose.
Substituting a sweetener that is mostly sucrose (table sugar, maple syrup) or fructose (agave nectar, 90% fructose) will not work. If you do not use the proper substitute, the fat will separate out of your caramel and the caramel will either end up brittle, or too greasy to stick to your apples. Sucrose is a disaccharide of fructose and glucose; in other words, sucrose is fructose linked to glucose. With caramel apples, the glucose essentially keeps everything in solution. Sucrose has a completely different structure. If there is not enough glucose, the sucrose recrystallizes and the fat gets pushed out of the caramel, and you do not have that chewy creamy goodness. So what is the magical mother nature substitute for corn syrup? HONEY! Honey has about the same glucose and fructose content as corn syrup. It took me 59 caramel apples worth of experimentation, but at the end of it all, I came up with a repeatable recipe for caramel apples that does not include any corn syrup or high-fructose corn syrup.
This video shows a condensed version of the process. The footage is from one of my experimental batches using corn syrup in order to observe the properties of that kind of caramel. Just pretend that I'm adding half a cup of honey instead of Karo syrup: