Hi there,
I tested the widget given what you described on my end. Let’s say I have a category of Family and a subcategories under Family as vacations and meals. If I set a visibility where I wanted the Family category to have the archives widget visible, then both vacations and meals should show the archives widget. In the categories module under each post, if I select Family, but not vacations and meals, that particular post should display the archives widget since it is under the family category.
So, unless I am understanding what you are looking for, as long as the category is selected to show a certain widget, all subcategories under that widget should display.
Hope this helps, let me know if you have any questions.