class Database extends OneDatabase
The good thing about this code is your bracing style which is applied consistently and is visually appealing.  Now on to some improvements:

This code does not implement a Database.  (You have called the class Database, but it does not resemble something that looks like a database).  This class does not really have a good purpose.  If you are going to write a database class it should handle database type things.  Like transactions or methods for select, insert and delete statements etc.

Some other things:


It is not easy to re-use the code.
It contains hard coded values.
It breaks up a logical separation of concerns for your program.
Don't use eval - it is not good for your application security:
eval("\$query = \"$query\";");
oneDatabase::$_database can be replaced by $this->_database as you
are extending that class.
mysqli is mixed in with PDO.  Just use PDO.
databaseCopy is not required
method access should be specified (public, protected, private)


In summary, I think you should re-think your design.