@thibou-justin, yea the first time you ssh into a remote box, it will ask prompt you to accept the server's fingerprint. If you hadn't done that first, that might be why the command wasn't working.
You definately do need root's local public key (id_rsa.pub) in the remote pi's authorized_keys file though. You could put it in root's or pi's authorized_keys file depending on which user you want to be able to login as on the remote pi.