Applescript: activating remote application failure
Thanks to @Tetsujin for this link which provided the details for the answer.

My script now looks like this:

tell application "iTunes" to quit
set remMachine to "eppc://user@0.1.2.3.4"
tell application "Finder" of machine remMachine
    open file "Macintosh HD:Applications:iTunes"
end tell

This does the following:


Quits the local instance of iTunes 
Sets the details of the 'remmachine' 
Opens iTunes on the remote machine