Context Filters Views Taxonomy Parent
That's quite tricky because the taxonomy system doesn't seem to like looking for children.  You might need to use Page Manager and the ctools context system to achieve this.


Create a 'page' (url) at /categories/%term-id that has the term currently being viewed as a context
Create a view pane that requires a context of parent term id which shows all nodes that have the taxonomy term subordinate to the parent term
use the view pane in your 'page' and set the context to the term being viewed


There's a rather good example of a similar use case here (watch the whole series, it's really good).