If I remember correctly, you first have to finish John's quest. Or at least get to the point where you can craft iron bars from John. You create them by clicking on the furnace behind John. Then you have to create a stove at the blacksmith. You could have already crafted this before, because it's the same item you craft for Mira's quest. You don't have to talk to the blacksmith, but you have to click on the anvil. From there, you'll create a copper oven. Once you've done that, you'll see that you can place it in the room to the left of the storage room. I don't remember if you have to ask Roderic to craft you a bathtub first.
Once you've installed the bathtub and the cupper oven, you'll need to insert iron bars into the ovan to keep the water alawes hot.
Also for the cat
By the way, I hope I'm wrong, but the cat outside the door doesn't appear until you've learned two things: how to make traps and, if I'm not mistaken, the store rabbit house for Emily's house. I remember that only after catching rabbits and mouse or chickens, the cat appeared outside the house.
This is one of the reasons why I ask Roderic to make 1 or 2 beds at a time

if you ask him for all the beds, it takes forever. And if you need it for something else, you can't do anything but wait.