This is also for my personal need in the future whenever i setup a cpanel server for my TWOPIZ HOSTING. There is a way to move mysql to other directory other than the one defined by cpanel. Firstly, you will need to backup everything on /var/lib/mysql folder. Once you have done that, you will have to follow the below instruction.
cd /var/lib service chkservd stop service mysql stop mv mysql /home ln -s /home/mysql mysql service mysql start service chkservd start
The backup apps will still work normally as the mysql folder still exist on /var/lib just that now it is pointing to the /home directory where the size is the largest.