It's actually pretty easy. All you have to do is go to the cat's house when he's not inside. Once you're inside, you'll get the key. After that, when the cat is in the white slime's house with her, all you have to do is stand right next to the door, open your inventory, and use the key. That way, the door will open on its own, and you'll be able to go in and see them. Very easy!!!
Just in case, do you happen to know where the secret boss is?