There is no easy way to do that. For each contact in a group, you can only choose one address to use via Edit Distribution List.
If you want to send it to all three addresses, create three groups and add each group to the address field. I tested this once when I dreamed it up years ago, and haven't tested again, so I don't know if it still works.
Another method is to just create the email with every address you want in the group. Select all of the addresses and drag them to the Desktop (or another folder). That will create a Text Clipping. Rename it so you can remember what the group is for.
You can then drag that text clipping into the address field of new messages and it will populate with all the addresses.
If you need to add or delete, drag it in, add or delete addresses, then select all and drag it to the desktop again.
Maybe it's just me, but if someone sent me the same email to all of my email addresses I'd put them on the auto-delete list.