Caramel without stirring or burning
First, it is very possible to make good caramel without stirring or burning. What you need is the right vessel and good temperature control. Choose a pot (or also a pan, if you won't be adding anything to the hot caramel) that has an even heat conduction without hot spots, and choose its size such that your sugar is less than 1.5 cm deep, but more than 3 mm. Then heat on mid-high, but do not go full strength on the burner. I use the dry method with this, and always end up with great caramel without any burning. 

The thickness of the sugar is very important, if you make it thicker, the bottom will turn to caramel and burn before the top has even melted. Less than 3 mm can work, but it goes through the stages so quickly that it is very difficult to work with. 

If you use this method, you will see the bottom getting liquid and coloring while you still have cold, unchanged sugar crystals on top. Do not stir them in! Just wait until they have melted naturally, no matter how  much it looks like it needs stirring. Else you end up with a mess. 

You can use this principle with the wet method too, especially if you are not making caramel but candies at a temperature below caramelization. You can have it deeper then, since the convection in the syrup helps the upper layers heat up. 

Once your caramel is at the needed point, you can start adding your dairy for making the soft caramels candies. 



My second point: I am surprised that you are getting that crystalization when stirring. It is common enough with sugar syrup, which contains water, but if you are heating with the wet method, all water should have gone before you enter caramel stage, and I haven't had candy crystalize on me at that point. So make sure you use a thermometer to determine when the caramel is ready for the next step, and that you are adding sufficient dairy.