Your best option: change hosting providers.
Short of that, MySQL replication is probably the best option here... If that's not an option because of the hosting provider... you could:
a) Setup a cron job to sync the databases instead of you having to manually do it via SSH.
b) I'm sure that instead of direct calls to mysql_query(), mysql_connect(), etc. you're following the good advice of using some sort of database abstraction or wrapper function. In this case, say you have a function like this:
function execute_query($query)
{
return(mysql_query($query));
}
You could modify it to do this:
function execute_query($query)
{
mysql_query($query, $the_connection_for_your_backup_host);
return(mysql_query($query, $the_connection_for_the_main_hosting_provider));
}
That way... you have both databases being updated in real-time and always in sync with each other.