the situation is:

I am trying to ask the apartment manager for a key to open the
door of a fence around the pool.

Which one is popular one? If they are all wrong, what is the correct way to say?

1. May I get a key to the door of the fence around the pool? (too formal)
2. May I get the swimming pool key? ( swimming pool can't have a key.

3. May I get the key to access the swimming pool?