Roo, I think you’ve hit on a big theme re the male v. female dynamic. It’s like there’s a patriarchal and matriarchal construct which interweaves with the other big theme: Employer and Employee, Rich and Poor, Euro-Mexican and Indigenous People. Lots of duality in this movie.
You mention dogs. Yes, lots and lots of dogs. But what about water? It’s one of the very first images in the movie (Cleo mopping the floor). Rain. Bathing. Washing dishes. Washing clothes. Dripping water from the clothesline. All building toward that sequence at the sea.
Another thing: This feels like a story where Cleo and Sofía have gone through their own arcs, Sofía in some ways a more significant one than Cleo, but in the end, the relationship between the two doesn’t really seem like it’s changed. Sofía will still be the Employer, Cleo the Employee. No matter how dramatic their shared experiences (Sofía helping Cleo through her pregnancy, Cleo standing by Sofía during her adjustment to being left by Antonio and saving her children), their external circumstances remain the same. I wonder if this is perhaps the biggest point — if Cuaron is trying to make a point — in the movie: Things change, but don’t really change.