Two layer multisite

I’m looking for suggestions, and if WordPress isn’t an ideal choice, I’m open to all suggestions. I am thinking of a wide array of sites, and basically a double multisite option, with sub sites having parent and child sites, and initially multisite module seemed like a good fit, but there are some aspects that don’t seem to work as I had hoped.
Here is an example of the original thought:
Dogs.mysite.com (parent)
? LabradorRetriever.mysite.com (child)
? GermanShepard.mysite.com (child)
? Bulldog.mysite.com (child)
…and so on…
Cats.mysite.com (parent)
? Siamese.mysite.com (child)
? Persian.mysite.com (child)
? Mainecoon.mysite.com (child)
…you get the idea
And a secondary option is the naming format dogs.mysite.com/LabradorRetrievers, and I could point the subdomain as needed.
? Now one limitation with multisite is that I want the parent to control some aspects of the subpages, such as index page having a shared post between parent and all child pages; I’m aware this may be frowned upon by search engines. This might be defined by post category. The main primary homepage/site should encompass all categories.
? A second limitation is that I would like to list all the child sites on the parent site, as well as list the parent and all child sites at the footer of each. Furthermore, on this, I would like the primary domain to list all the parents in a similar fashion.
? Each site should have its own index. (landingpage, custom menus, subpages…)

Thoughts?