I have a remote server to which I need to connect to. Let's say the hostname is Remote01. From my local, I am connecting to it via a VPN (Juniper). I have another remote server in my intranet which is an RHEL server. I loginto this RHEL server (let's call it Remote02) and in the command line I type:
ping Remote01
This returns
ping unknown host Remote01
Do I need a VPN installed in Remote02 as well?
You would need to install the VPN client on Remote02 as well in order to reach Remote01.
Or, if you're comfortable changing the routing table and firewall of your own server/machine, you can changing the routing table on Remote02. For the network of Remote01, instead of going to the default gateway, point it to your local machine. On your local machine, modify the firewall to accept incoming packets from Remote02 to forward to to Remote01 via the existing VPN connection.
I would say the first solution is much simpler. But if for some reason, the VPN client is not available on Linux then you can try the second solution.