zota marius on "Connecting to on-line MySQL database"

From your web arhitecture "Customer's computer <<>> WordPress <<>> MySQL database." i don`t understand your question very well what you want exacly to do, but Granting access to a user from a remote host to a mysql database is fairly simple . First you will need to login to your MySQL server as the root user. Once you are logged into MySQL you need to issue the GRANT command that will enable access for your remote user.

something like this

mysql> GRANT ALL ON xxxDatabase.* TO xxxUser@'1.2.3.4' IDENTIFIED BY 'my_password';