I think there must be lots of easier ways to achieve this. How about:

If you're running a sendmail daemon rather than using POP/IMAP to fetch the
mail then one could just create an alias (e.g. in /etc/mail/aliases)
to map the shared email box name into the usernames of each
family member, so everyone gets sent a copy of the mail when it arrives.

If you are not running a sendmail daemon, use fetchmail to
retrieve the mail and then feed messages from fetchmail directly into /usr/sbin/sendmail
and again use an alias to send copies to each family member.
For help on fetchmail, try
man fetchmail in a terminal.

Mail.app preferences should then setup without a POP/IMAP entry -
leaving just a "Personal Mailboxes" entry which tells Mail.app to read new
mail from /var/mail/username.

Note that to use personal mailboxes under the public beta you need
to make /var/mail writeable by everyone but not trashable by everyone, otherwise
Mail.app fails because it can't modify your personal mailbox file (/var/mail/username) (note
this is a bug in Mail.app).
To change the directory permissions from a terminal, first change to the root user with
su (and respond with the root password) then type chmod 1777 /var/mail
and then exit to finish working as root.