SSHd restriction per user basis

Are you sure that root login to ssh is allowed?

Check sshd_config and verify that root login is permitted. sshd will need to be restarted if the setting changes.

As you mentioned, the environment variables are removed by sudo, for security reasons.

But fortunately sudo is quite configurable: you can tell it precisely which environment variables you want to keep thanks to the env_keep configuration option in /etc/sudoers.

For agent forwarding, you need to keep the SSH_AUTH_SOCK environment variable. To do so, simply edit your /etc/sudoers configuration file (always using visudo) and set the env_keep option to the appropriate users. If you want this option to be set for all users, use the Defaults line like this:

Defaults    env_keep+=SSH_AUTH_SOCK

man sudoers for more details.

You should now be able to do something like this (provided user1's public key is present in ~/.ssh/authorized_keys in user1@serverA and user2@serverB, and serverA's /etc/sudoers file is setup as indicated above):

user1@mymachine> eval `ssh-agent`  # starts ssh-agent
user1@mymachine> ssh-add           # add user1's key to agent (requires pwd)
user1@mymachine> ssh -A serverA    # no pwd required + agent forwarding activated
user1@serverA> sudo su - user2     # sudo keeps agent forwarding active :-)
user2@serverA> ssh serverB         # goto user2@serverB w/o typing pwd again...
user2@serverB>                     # ...because forwarding still works