Without some sort of mailing list software, I'm not sure you'll really get the functionality you want.
As a workaround I would try setting up a custom tag, using an existing unused field, or something in Notes, and then creating a Smart Ground around that.
For example, all the contacts you want in your group, put 'mailing list' into their notes. Then create a SmartGroup to show those contacts.
Send the contacts to your friend, and they can import and merge the data. If they setup the same smart group, you should have the same contacts, with the same info, in that group.
The other option would be to stop her importing anything, and just use a Shared Addressbook, and maintain everything there. Google, Exchange, LDAP etc will let you use a remote address book, that isn't automatically synced to your local address book, but all contacts are accessibly, so you can both use that. In the groups page of the address book you'll see your local contacts, and remote contacts as distinct lists. Then, you'll just know to send to everyone in that shared address book.
Best Answer
Try creating a duplicate of the group and trying again to see if it the duplicated group works. Also, check that all the contacts have a valid email address on their contact card as this could be what is causing issues with the Mail App.