Transfer selected information from a SQL Server business server to a MySQL web server?
I've had to do this a couple of times, with varying complexity. My typical approach is to install the MySQL ODBC connector on the SQL Server host, create an ODBC DSN to the MySQL database, then set it up as a linked server in SQL Server.

Once that's out of the way, you can write T-SQL procedures/scripts to synchronize and replicate the necessary data.