Why do my caramels turn out hard in the center?

The higher the temperature, the harder the caramel. That is basically the whole story. So I think what is happening to you is that the caramel in the middle is still going up in temperature due to residual heat, while the stuff at the sides cools down quickly because it can vent heat through the pan to the outside world. Have you checked the calibration on your thermometer? In any case, I think the things you can try are (1) cook to a slightly lower final temperature (back down a couple degrees at a time) and (2) set the pan over a tray of ice to cool it more evenly. Also, be sure to do a really good job of that final stir before pouring into the tray.

As others have said, temperature is the key to the firmness of caramels, but not to the texture of caramels. You mentioned the inside is grainy. If that's the case, you might be getting incorrectly crystalized sugar in the center of the pan. One of the tricks to making caramels is to never scrape the pan. Let as much of the caramel flow out of the pan as possible, but don't scrape down the sides into the cooling dish. If you do, part of the caramel will turn grainy in about a day.

As far as temperature, forgot the thermometer. Temperatures vary by your altitude and the exact ingredients you are using among other things. Unless the recipe was written by someone who lived in the same house, used the same pans, and bought the same brands of ingredients, the temperatures should be considered a very rough estimate. Get a bowl of ice water and keep it nearby while the caramel is on the stove. Periodically drop a small amount of the caramel into the ice water and give it a few seconds to cool. Pick up the drop of caramel and see if it is the texture you want.

Summary:

• Don't scrape the sides of the bowl. Throw that part of the caramel out (or eat it straight from the bowl).
• Drop bits of the caramel in ice water to check the firmness while cooking. This method is far more reliable than a thermometer. (But don't burn yourself!)

Don't scrape out the pan. Stir it as you remove it from the heat and pour. DON'T scrape. The residual caramel is still cooking and will be harder than the rest.

I would think if an area of the product is harder than the rest then it will be due to cooling issues.

If the external areas are softer, then it should be the case that they did not reach as high a temperature as the centre or have cooled at a different rate. Central bottom areas of the pan are liable to cool more slowly, as they have are insulated by the other material and have less ability to diffuse the heat. Perhaps putting the pan on something heat conductive, to draw away heat underneath may help.

The other major issue is the cooking itself. If your pan is too wide, or too thin based (it needs to be thick, or the heat will not be even), then it is normal to have widely different heats within the pan. Some areas may be much hotter than others. Make sure your sugar thermometer is accurate (you can do that roughly by placing it in rapidly boiling water and ensuring the temperature is about 100C), and ensure that it is reasonably deep in to the mixture.

Points to examine:

• Are you checking your temperatures right up to the moment you take them off the heat?
• Are you arresting the heating process, via cold water submersion of the pan or other method?
• Are you over/under stirring, particularly near the end (have you watched your mum make these?)
• Is the pan you use very differ to that which your mum uses? (As this will effect cooling rates, particularly if the dimensions are different which effects the depth or surface area - the base thickness is very important).
• Where does she cool hers?
• Is your thermometer accurate?

If it makes you feel any better. Chewy caramels are really hard in my opinion, the recipe is simple, but experience counts for a lot. I totally burnt a few batches initially when trying to cook them.