A *user* is not a *type* of database so the relationship makes no sense. A user might depend on a database, but that is as far as the relationship should stretch.
As for your issue:
Firstly, you reference methods and properties declared within a parent class using $this not parent. Just as you would any local method or property. The only time you need to use *parent* is when you are overriding a parents method and within that child method you need to call the original parent method.
Secondly, you have not implemented the child __construct in such a mannor that you will be able to create a database object.
These two points are mute however as like I already stated, user should not be extending database.