I moved your duplicate post back to your original post.
I believe your problem is this:
When you add a Rich Text Element to a CMS template, you can assign a class to the element, but you cannot style its children since the content is loaded from the CMS when it is bound to a rich text field in the collection.
Un-bind the element and then apply your nested styles. When you are done, bind the element again.
My preference is to style items in my designs by placing the element on a style guide page where I add the class(s), and in the case of a RTE, all the nested styles. Then when I need to reuse the styled element, I just apply the style(s) to a new instance or copy and past it.
This way, I always have a current reference I can visually inspect. This is also very helpful when using combo classes.