Caramel Sauce to Butter or Not to Butter

I make an amazing Caramel Sauce, but I am torn between adding a small amount of butter. When I add butter it seems to not incorporate fully. Meaning there is a slight oiliness on the surface of the finished product or when it cools small dots of white oil from the butter in the product sometimes, as well. I normally add the butter to the caramelized sugar with the cream and the mixture is then cooked to the desired thickness so that the extra water in the butter will cook out. I have tried different brands of butter. Also, I have added a minuscule amount of sunflower lecithin as an emulsifier(which totally works), but I would rather not. I want a sauce with only cream, sugar, vanilla and sea salt, and maybe butter.