How to make MySQL log to 2 separate remote servers?
The .mysql_history file is only for commands in the mysql client, and only for the current operating system user. I don't know of any way to log this anywhere but in .mysql_history.

The mysqld.log can be written to the local syslog daemon, so it ends up in /var/log/messages (or wherever you send syslog). You enable this with the following entries in /etc/my.cnf:

[mysqld_safe]
syslog
syslog-tag = mysql


The syslog-tag is optional, but helpful so your mysql log entries are easily separated from other syslog entries. I like to name the tag something specific to the server, if I'm going to merge mysql logs from multiple instances into one remote syslog.

Then you can use rsyslog to send the syslog content (or only the subset of entries with the given tag) to another server. See http://www.rsyslog.com/storing-and-forwarding-remote-messages/



This question might also be helpful: send logs to multiple rsyslog servers