If the middle button makes the outer button related to it (and it can do so, in three different modes – private, public and protected), then, it only stands to reason, to go ahead and document that relationship. Depending on how their inheritance relationship was tagged, you will have to list down what is private data (variables and functions) to the outer button.
Now, if the innermost button inherits from the middle button, then it too will have rules of engagement not only from the middle button, but yes, from the outer most button too. A private relationship, means that everything (variables and functions) are private to the class only.