Have a look at INNODB and hot copy. It's a rolling backup. Using mysqldump 4 times a day will kill your site (obviously). You're locking the tables while mysqldump dumps over a million posts. That probably takes 2 hours or more. 4 times a day. So, for 8 hours a day your database is locked. No wonder it's dead most of the time. Look into alternate methods of backing up this data. Seriously.
Of course a huge and significant prune would also fix it, but that's a different discussion.
