Your recipe seems fine. Are you weighing or doing volume measurements for the major ingredients? Weighing is preferred. Are your leaveners fresh? Toss 'em after a year, get new ones, and highlight the expiration dates. How do you grease your cake pans? Use a solid shortening, such as butter, margarine or Crisco. Oils and oil sprays sometimes don’t release the cake as easily as they should. Make sure your pans are lined with waxed paper or baking parchment on the bottoms to help with the release.
Perhaps you are not baking your layers long enough? Maybe your oven temperature is too low, or erratic, check it with a thermometer. Also, bake your layers side by side, not one on top of the other. Switch them around about halfway through the baking time(be quick as a bunny)
Try this trick: beat the eggs in the mixer bowl first, about one minute. Add the sugar slowly, beat till creamy. Add the oil(I recommend Crisco oil) VERY slowly in a thin stream, as if you were making mayonnaise. Next the sifted dry ingredients, about a 1/2 cup at a time. Then the grated carrot(make sure they are medium-ground on a box grater or in a food processor, using the steel blade, no long shreds please) Finally the nuts, raisins, whatever. Divide the batter exactly, weigh it if you have to. Or, bake all the batter in a tube pan, the central core will help the overly-moist batter bake thoroughly. Cool layers for 20 minutes, tube pan about 30.
I’ve been using my same recipe and directions for 50 years, and have never had a failure.