In the documentation for DBD::mysql for the connect() method, there is the following:

mysql_socket

As of MySQL 3.21.15, it is possible to choose the Unix socket that is used for connecting to the server. This is done, for example, with

    mysql_socket=/dev/mysql

Usually there's no need for this option, unless you are using another location for the socket than that built into the client.

(Untested, but) I believe setting this to path of your new socket may resolve your issue. (The documentation for mysql_read_default_file, located just above it, explaining why this may be the case.)

Hope that helps.