Firstly, search all of the currently available locations in Cape Coocoo. Use spacebar to reveal hotspots. If you touch everything, you'll collect an item that will allow you to open the gate.
I need another hint about unlocking the gate.
If you can't find a key, you may need to take a more forceful approach.
I need a spoiler about unlocking the gate.
Forget trying to unlock it and smash it with the Hammer!
Where is the Hammer?
The Hammer is found in a toolbox inside Ye Olde Coocoo. (The bar.)