CMS-bound Rich Text Elements ( RTEs ) behave differently in the designer.
When a rich text element is CMS bound, you lose the ability to select any of the sub-elements, and do any styling work in the designer.
The solution is to maintain a "copy" of that RTE on a hidden static page, with the same Class. Keep that RTE un-bound, and you'll be able to select and style sub-elements normally.
Because your CMS-bound one uses the same Class, any styling changes you make to your hidden copy will appear on the CMS-bound one as well.
You can mark it as Draft, since you will only need to access it in the designer. I usually have a Style Guide folder, and then have several pages in it, e.g. a blog page, a product page, etc, along with the special styling mechanics I need to centralize there.
In your style guide RTE, put all of the elements that you might use in the CMS, and style all of them;
Anything you could conceivably use, put it in your style guide RTE, and style it to make sure it looks OK.
Try different arrangements as well, such as putting an H1, an H2, and an H3 next to each other. Or putting an image next to an unordered list. You need to see how these variations will look, and how the spacing will work.