I have a new theory on this: we have seen the missing child many times throughout the series, and didn't know what we were seeing. It has all become clear to me now, though. The child in question is, in fact: Hallie!
Now, hear me out on this:
- Hallie is of such indeterminate breed, because she's actually not a dog at all.
- Hallie has been manipulating events from the beginning, and convinced Violet in the pilot to stay in the house after coordinating with Infantata, Troy and Bryan, and Beauregard in the basement.
- Adelaide was just trying to greet her long-lost sibling.
- Hallie was under the table at Langdon family dinner night, which is why we didn't see her.
- Hallie is the last surviving child of Constance, left behind with Marcy to protect Constance's interests in the house.
So, this makes as much sense as most of the runaway theories. Anyone want to take a shot at disproving?