I have a box on a network that is only accessible via connecting to multiple SSH boxes in succession. the "-t" option in ssh allows me to go straight through all the boxes using one line:
ssh firstname.lastname@example.org -t ssh user@homeserver -t ssh user@home-desktop
You literally just chain together as many ssh connections as you'd like. They just pass the arguments on and on. If you alias that to something like:
et-phone-home="ssh email@example.com -t ssh user@homeserver -t ssh user@home-desktop"
then you should be all set.