transferring data from one mySQL server to another?

I need to duplicate the data from one mySQL server (where my wife's domain is hosted) to another machine (under my control) for backup and possible relocation purposes. My biggest stumbling block is that I can't access either server remotely (ie. I have to log into both mySQL servers using localhost as the host name). I figure I can hard code the table building code without too many problems. I can get all the data from the current web server and get it in an array (at least I think I can) and I should be able to pull the code from the array and insert it into the server under my control. The part I can't figure out is the in-between part. Should I run a PHP script on the remote (to me) server to write the data to a file (I've never tried writting data with PHP), then ftp the file to me an run a PHP script locally to read in the data or is there a better way? Any suggestions will be greatly appreciated. John Guynn