You can use Net::OpenSSH::Gateway.

It never went into CPAN because I was unhappy with its internal architecture and was planning a complete revamp, but unfortunately never got the time/guts to actually do it.

In any case, it works reliably. Just install it and tell Net::OpenSSH(::Parallel) to use it with the gateway option:

$pssh->add_host($secondary_server,
                gateway => { proxies => "ssh://$primary_server" },
                ... );
[download]

Or in case you want to pass additional options when constructing the underlaying Net::OpenSSH object used to connect to the primary server:

$pssh->add_host($secondary_server,
                gateway => { proxies => { url => "ssh://$primary_serve
+r",
                                          user => $primary_user,
                                          password => $primary_passwor
+d, ... } },
                ... );
[download]