Once you complete the scooter chase, you return to the museum, and receive a package. The message says to go to the museum Early Poptropica island. When you go there, the curator of the Museum Fantastique gives you a key.
Since you have been looking for the key to the cottage in the Country Side (the Inspector's house), try the key there.
You use it.
You use the key from the Curator to unlock the Inspector's house in the CountrySide.
Once you get the key from the curator, go back to Counterfeit island and use it at the Inspector's house.
If your talking about Counterfeit Island then you get the key and go back to the museum on Counterfeit Island
The key to the investigator's chest on Counterfeit Island is hidden in the bushes to the right of the cottage. You need to use a stick to reach it and then unlock the investigator's chest to get the next clue.
a girl named paisley
Early Poptropica.
The same way you got in to get the picture piece : use your key.
You take it back to counterfeit Island and use it on the door of the house.
Use the key she gives you to open the inspector's house in the Countryside.
The key fits the Inspector's cottage in the Countryside.
The old woman is the curator of the museum on Counterfeit Island, and she came to Early Poptropica to recover a key you will need to complete the quest. When you receive her message, go there, get the key, then return to Counterfeit Island to use it at the Inspector's house in the Country Side.