On the category page for the cemetery, you need to put the tag
[[Category:Franklin County, Vermont, Cemeteries]]
That will make the cemetery category show up as a subcategory on the Franklin County, Vermont, Cemeteries category page.
When you put the category tag above on the free space page, it makes the free space page show up as a page on the Franklin County, Vermont, Cemeteries category page.
I feel like I'm still not saying it clearly enough - is this any better?