How to not burn the sugars in veggies when simmering in a dutch oven for a long time?

It sounds like either your heat is too high, or there is not enough liquid in your stew. If you can't reduce the flame, consider a heat diffuser.

You should mix the stew once in a while so everything has a chance to be at the bottom of the pot. A silicone spatula is good for scraping the bottom cleanly and getting those ingredients up and mixed around. Fold like you would an angel food cake and it won't take much mixing each time.

From my experience, I believe it to be the sugars and proteins in whatever liquid you're cooking in that is what's actually burning, and not the vegetables themselves.

You can try a few things:

1. As @myklbykl mentioned, stir frequently. I typically aim for every 15 minutes, but my stews typically take more than an hour, not 30-40 minutes. For yours, you might want to aim for every 5-10 minutes. I also like a spatula, as the flat end helps you to make sure that you're scraping the bottom well. (but I use wood, not silicone)
2. Turn the heat down. You don't actually want to see the stew vigorously bubbling. You typically want to see an occassional bubble, which for most stoves, if you have a well-fit lid is low or warm, not 'medium'.
3. Move the pot to the oven. I know you said wanted to do it on the stove-top, but the more even heat means that you can keep the oven pretty low and not have the temperature gradient that you would by cooking it on the stove.
4. Add your potatoes later. If they're breaking down on you, this will thicken the liquid and make it more likely to burn. Instead, cut them smaller and add them later.
5. Change your potatoes. Again, if they're breaking up on your, change to a 'waxy' (roasting) potato instead of a 'floury' (baking) potato. If the stew still isn't thick enough for your liking five minutes before serving, take a box grater and grate a potato straight into the stew ... it'll act like instant mashed potatoes and thicken up quickly.