Without seeing the result and knowing your exact technique, my best guess is that you're not using enough liquid, or that you're using heat that's too high. High heat will essentially fry the onions, like you would expect by dropping chicken or potatoes into a pan full of hot oil.
Properly caramelized onions should take at least 20 to 30 minutes, I try to go for an hour whenever time permits. I actually stir as little as I can without allowing them to sit long enough to burn. Over-stirring shouldn't be a problem; under-stirring may be.
To start, you want the bottom of the pan to be covered with a thin layer of oil, and then make sure you stir the onions very well to coat them completely right after you toss them in. Begin with the pan on medium-high heat to get the oil up to temperature, once it ripples and you put the onions in you can lower it quite a bit. I rarely put it above 5 (out of 10, glass-top stove), and if I see things going crispy, I'll often drop it to 4. I'd rather take more time and have softer onions.
Are you adding any liquid along the way? Sometime, when doing large batches, 15 minutes in I find that I don't have enough oil in the pan, and I can see them starting to crisp up a bit more than I'd like. When that happens, lower the heat a notch, and add a touch more oil (or, as I prefer, a cube of homemade stock) to the pan. It'll take some practice, but eventually you'll be able to know how much liquid to use instinctively. The reason I prefer stock for my "second add" is because I know the stock will evaporate off, as mentioned in the question you linked to, you don't want to be pouring off flavor at the end of the cooking time, so evaporation is a good thing!
If you're using cast iron, I recommend trying stainless steel, I get much better results with the latter than the former. I'd guess that it's because I can dynamically regulate the temperature better with the stainless steel - with cast iron, once you realize you're at too high of a temperature, it's hard to lower it quickly.
If you need a step by step guide to start you off until you get a feel for everything, there is a great guide here and another here. The difference is that one recommends 1 teaspoon of oil per onion; the other uses 3 tablespoons per onion. I find that for my kitchen, it's somewhere in the middle (I just eyeball so I can't give you an exact number, unfortunately) - but if you try both methods on your stovetop you should be able to use that data to determine the right amount for you.
Save the veggies in a freezer bag or air-tight bowl (in the freezer) and when it's full you've got most of vegetable soup without it taking so long.
Additional veggies that taste amazing after being slow-cooked with meat for 12 hours: rather, ask, Are there any veggies that won't taste amazing?
Best Answer
Carrots and onions have different cooking times, so no, you can't throw them together.
What I would do is cut the carrots as small as the onions (just for aesthetic purposes), start stewing the carrots in a closed pot first and season them as you like, and when they're nearly done, add the onions and caramelise them normally while they're stewing together with the carrots and you'll end up with caramelised carrot-onion stew.
Obviously, you can always cook them separately and then mix them just before serving, but that would take an additional pot and I don't like doing dishes... ;-)