The key to the Inspector's house is given to you by the museum curator after you chase the thief on Counterfeit Island. The sign is rather obvious, since "Veuve Noire" is French for Black Widow (it is misspelled 'niore').
(After the scooter chase, get the package at the museum. Do what it says and you'll get the key to her house.)
Go back to Counterfeit Island and use it to open the Inspector's house in the Country Side. On the way, the street artist gives you a clue as to what to look for in the house.
the chest is just a distraction
Use the key she gives you to open the inspector's house in the Countryside.
The art thief is back on Counterfeit Island. As part of Counterfeit island, you don't need to do anything in Early Poptropica except get the key from the curator at the Pop Art Museum, then return to Counterfeit Island to open the Inspector's house.
there is no curators house. if you're talking about the dectives house on counterfeit island, you don't open it. you peel the painting off the scream by a "slightly peeled corner".
The art museum on counterfeit island opens after you go to the guy at the dock.
There is no key to the chest and no way to open it. It is just a distraction. (The actual item in the house is the gaudy painting on the second floor.)
It doesn't have a key, it's there to distract you; you don't need to open it.
I forget but I think the lady in the museum gives the key to you...
In the Inspector's house, ignore the chest because there is no way to open it. Go to the painting on the second floor and peel back the corner.
The "assistant curator" will offer you a job if you correct the hanging artwork (move them clockwise to the correct galleries). After you get the key from the curator on Early Poptropica, return to Counterfeit Island and use it to open the Inspector's House.
you go out the door!