The daycare in Solaceon town was taking care of my Swablu for a while, but when I came back for her I discovered that she had forgotten Sing in exchange for natural cure. This made me pretty annoyed, but what even is the daycare protocol for a Pokémon learning a new move? Can the daycare let her forget moves without notifying me?

Unfortunately yes. You see, the daycare owners aren’t actually training your pokémon; rather, they’re letting them roam about a field alongside other pokémon. They are, of course, feeding and caring for your pokémon and ensuring that they don’t run away or injure each other, but the point is, no formal training is involved. So consequently, except for Alola’s daycare (which is actually just a breeding facility), pokémon are allowed to spar and interact with one another, which could result in not only added experience but also the learning (and unlearning) of moves. Typically, daycare owners don’t keep track of this unless the new move is particularly destructive and has posed a danger either to the user or the other charges.

In short, the daycare owners aren’t to blame here, I’m afraid. It’s just that your swablu has been particularly precocious.