How to display the MiniPlayer in iTunes with AppleScript?
AFAIK you can only do this using UI scripting, here are some ways to switch to the miniplayer : 

Simulating a click on the button in the interface : 

tell application "System Events" to tell process "iTunes"
    click button 4 of window 1
end tell


Using the keyboard shortcut : 

tell application "System Events"
    tell application "iTunes" to activate
    keystroke "m" using {option down, command down}
end tell




If you want to display the miniplay AND the fullsize player (your request isn't clear) use : 

tell application "System Events"
    tell application "iTunes" to activate
    keystroke "3" using {option down, command down}
end tell