Is SNMP a solution

I have a xymon server located out in the Internet that uses custom scripts for monitoring. I monitor this one server which is NATed behind a firewall. I use 'xymon-rclient.sh' script to fetch the data. This server is only one that is exposed on the internet, it has an IP of 192.169.100.50. But I want to monitor it's sister server '192.168.100.51' which is not exposed on the Internet. Somebody said to me that SNMP might be a solution. If that is a solution, can somebody give me a high level explanation on how this might work? Thanks in advance.