You didn't say why you didn't want to log into one host and then copy to the other so I will share one of my reasons and solutions.

I couldn't log into one machine then rsync to the other because neither host had a SSH key that could log into the other. I solved this by using SSH agent forwarding to allow the first host to use my SSH key while I was logged in.

WARNING: SSH forwarding allows the host to use your SSH key for the duration of your login. While they can't copy your key they can log into other machines with it. Make sure you understand the risks and don't use agent forwarding for machines your don't trust.

The following command will use SSH agent forwarding to open a direct connection from host1 to host2. This has the advantage that the machine running the command isn't bottlenecking the transfer.

ssh -A host1 rsync -vuar /var/www host2:/var/www 

You didn't say why you didn't want to log into one host and then copy to the other so I will share one of my reasons and solutions.

I couldn't log into one machine then rsync to the other because neither host had a SSH key that could log into the other. I solved this by using SSH agent forwarding to allow the first host to use my SSH key while I was logged in.

WARNING: SSH forwarding allows the host to use your SSH key for the duration of your login. While they can't copy your key they can log into other machines with it. Make sure you understand the risks and don't use agent forwarding for machines you don't trust.

The following command will use SSH agent forwarding to open a direct connection from host1 to host2. This has the advantage that the machine running the command isn't bottlenecking the transfer.

ssh -A host1 rsync -vuar /var/www host2:/var/www