If the second node cannot ping the IP address of the SMTP server then it seems likely that there is a problem with the routing configuration or that communication is being blocked somehow e.g. by a firewall
So that is one issue. You can debug that as a networking problem e.g. Is routing involved? Are the Filers on the same subnet? The SMTP server also?
Secondly it seems that the autosupport message is not being delivered from either node. In my experience SMTP servers often reject messages because of "anti-spam" configuration options e.g the server may require a specific "from" address. Have you configured the autosupport related options? E.g. in 7-mode (I don't have access to a CDoT Filer at the moment - sorry) there were options such as:
If you can get to see the SMTP server logs it is very helpful e.g. you should be able to see if the Filer(s) are even able to connect.