What is a term for the hierarchical relationship between parent and child configuration options in software?

The nomenclature of a "parent" and a "child" implies that what affects the parent will influence the entirety of the children. Therefore, I would suggest eliminating any clarification.

"Enabling or disabling the parent option enables or disables all child options as well."

If your audience is technical users, most would consider this to be recursion. If you're operating on a directory and all of its subdirectories, for example, you would use a "recursive" command line option:

Enabling or disabling the parent option recursively enables or disables all child options as well

Enabling or disabling the parent option, enables or disables all related child options as well.

Also the word cascading comes to mind

I would use recursively, although "cascading" does convey much of the meaning, that is used more often in user interfaces in my experience.

I would assume you actually mean all children and grandchildren, etc. So I would use something like:

 "Any change to an option sets or resets all its sub-options too."